On the Approximation of Complicated Dynamical Behavior
Abstract
We present efficient techniques for the numerical approximation of complicated dynamical behavior. In particular, we develop numerical methods which allow us to approximate Sinai--Ruelle--Bowen (SRB)-measures as well as (almost) cyclic behavior of a dynamical system. The methods are based on an appropriate discretization of the Frobenius--Perron operator, and two essentially different mathematical concepts are used: our idea is to combine classical convergence results for finite dimensional approximations of compact operators with results from ergodic theory concerning the approximation of SRB-measures by invariant measures of stochastically perturbed systems. The efficiency of the methods is illustrated by several numerical examples.
MSC codes
Keywords
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Michael Benedicks, Lai‐Sang Young, Sina‐Bowen‐Ruelle measures for certain Hénon maps, Invent. Math., 112 (1993), 541–576
2.
Michael Blank, Gerhard Keller, Random perturbations of chaotic dynamical systems: stability of the spectrum, Nonlinearity, 11 (1998), 1351–1364
3.
Rufus Bowen, David Ruelle, The ergodic theory of Axiom A flows, Invent. Math., 29 (1975), 181–202
4.
P. Chossat, M. Golubitsky, Symmetry‐increasing bifurcation of chaotic attractors, Phys. D, 32 (1988), 423–436
5.
Michael Dellnitz, Andreas Hohmann, The computation of unstable manifolds using subdivision and continuation, Progr. Nonlinear Differential Equations Appl., Vol. 19, Birkhäuser, Basel, 1996, 449–459
6.
Michael Dellnitz, Andreas Hohmann, A subdivision algorithm for the computation of unstable manifolds and global attractors, Numer. Math., 75 (1997), 293–317
7.
Michael Dellnitz, Andreas Hohmann, Oliver Junge, Martin Rumpf, Exploring invariant sets and invariant measures, Chaos, 7 (1997), 221–228
8.
M. Dellnitz and O. Junge, Almost invariant sets in Chua’s circuit, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 7 (1997), pp. 2475–2485.
9.
M. Dellnitz and O. Junge, An adaptive subdivision technique for the approximation of attractors and invariant measures, Comput. Visual. Sci., 1 (1998), pp. 63–68.
10.
J. Ding, Q. Du, T. Li, High order approximation of the Frobenius‐Perron operator, Appl. Math. Comput., 53 (1993), 151–171
11.
J. L. Doob, Stochastic Processes, John Wiley, New York, 1960.
12.
M. Eidenschink, Exploring Global Dynamics: A Numerical Algorithm Based on the Conley Index Theory, Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA, 1995.
13.
Rabbijah Guder, Michael Dellnitz, Edwin Kreuzer, An adaptive method for the approximation of the generalized cell mapping, Chaos Solitons Fractals, 8 (1997), 525–534
14.
C. Hsu, Global analysis by cell mapping, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 2 (1992), 727–771
15.
Fern Hunt, Approximating the invariant measures of randomly perturbed dissipative maps, J. Math. Anal. Appl., 198 (1996), 534–551
16.
Alexander Khibnik, Dirk Roose, Leon Chua, On periodic orbits and homoclinic bifurcations in Chua’s circuit with a smooth nonlinearity, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 3 (1993), 363–384
17.
Yuri Kifer, General random perturbations of hyperbolic and expanding transformations, J. Analyse Math., 47 (1986), 111–150
18.
Tomás Caraballo, José Langa, James Robinson, Upper semicontinuity of attractors for small random perturbations of dynamical systems, Comm. Partial Differential Equations, 23 (1998), 1557–1581
19.
Yuri Kifer, Computations in dynamical systems via random perturbations, Discrete Contin. Dynam. Systems, 3 (1997), 457–476
20.
E. Kreuzer, Numerische Untersuchung nichtlinearer dynamischer Systeme, Hochschultext. [University Textbooks], Springer‐Verlag, 1987xviii+194
21.
Andrzej Lasota, Michael Mackey, Chaos, fractals, and noise, Applied Mathematical Sciences, Vol. 97, Springer‐Verlag, 1994xiv+472, Stochastic aspects of dynamics
22.
R. B. Lehoucq, Analysis and Implementation of an Implicitly Restarted Arnoldi Iteration, Rice University Technical Report TR95‐13, Houston, TX, 1995.
23.
Takashi Matsumoto, Leon Chua, Motomasa Komuro, The double scroll, IEEE Trans. Circuits and Systems, 32 (1985), 797–818
24.
S. Meyn, R. Tweedie, Markov chains and stochastic stability, Communications and Control Engineering Series, Springer‐Verlag London Ltd., 1993xvi+ 548
25.
John Osborn, Spectral approximation for compact operators, Math. Comput., 29 (1975), 712–725
26.
David Ruelle, A measure associated with axiom‐A attractors, Amer. J. Math., 98 (1976), 619–654
27.
Ja. Sina, Gibbs measures in ergodic theory, Uspehi Mat. Nauk, 27 (1972), 21–64
28.
K. Yosida, Functional Analysis, Springer‐Verlag, New York, 1980.
Information & Authors
Information
Published In
SIAM Journal on Numerical Analysis
Pages: 491 - 515
ISSN (online): 1095-7170
Copyright
Copyright © 1999 Society for Industrial and Applied Mathematics.
History
Published online: 25 July 2006
MSC codes
Keywords
Authors
Metrics & Citations
Metrics
Citations
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited By
- Influence of uncertainties and noise on basins/attractors topology and integrity of Duffing oscillatorInternational Journal of Non-Linear Mechanics, Vol. 111 | 1 Nov 2023
- Global analysis of stochastic and parametric uncertainty in nonlinear dynamical systems: adaptative phase-space discretization strategy, with application to Helmholtz oscillatorNonlinear Dynamics, Vol. 111, No. 17 | 18 July 2023
- Efficient approximation of molecular kinetics using random Fourier featuresThe Journal of Chemical Physics, Vol. 159, No. 7 | 18 August 2023
- A Patch in Time Saves Nine: Methods for the Identification of Localised Dynamical Behaviour and Lifespans of Coherent StructuresJournal of Nonlinear Science, Vol. 33, No. 4 | 12 May 2023
- Analysis of low-order modal coherent structures in cavitation flow field based on dynamic mode decomposition and finite-time Lyapunov exponentPhysics of Fluids, Vol. 35, No. 8 | 4 August 2023
- Piecewise Monotonic Maps with a Common Piecewise Constant Stationary DensityJournal of Statistical Physics, Vol. 190, No. 8 | 20 August 2023
- Rigorous data‐driven computation of spectral properties of Koopman operators for dynamical systemsCommunications on Pure and Applied Mathematics, Vol. 3 | 27 July 2023
- Optimal Reaction Coordinates: Variational Characterization and Sparse ComputationMultiscale Modeling & Simulation, Vol. 21, No. 2 | 25 April 2023
- Learning to Forecast Dynamical Systems from Streaming DataSIAM Journal on Applied Dynamical Systems, Vol. 22, No. 2 | 5 May 2023
- Identification of the Madden–Julian Oscillation With Data‐Driven Koopman Spectral AnalysisGeophysical Research Letters, Vol. 50, No. 10 | 17 May 2023
- A general framework for the rigorous computation of invariant densities and the coarse-fine strategyChaos, Solitons & Fractals, Vol. 170 | 1 May 2023
- Optimal Transport for Parameter Identification of Chaotic Dynamics via Invariant MeasuresSIAM Journal on Applied Dynamical Systems, Vol. 22, No. 1 | 21 September 2023
- Koopman-Based Spectral Clustering of Directed and Time-Evolving GraphsJournal of Nonlinear Science, Vol. 33, No. 1 | 7 November 2022
- Maximally predictive states: From partial observations to long timescalesChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 33, No. 2 | 21 February 2023
- Optimal Linear Response for Markov Hilbert–Schmidt Integral Operators and Stochastic Dynamical SystemsJournal of Nonlinear Science, Vol. 32, No. 6 | 5 September 2022
- Dynamical geography and transition paths of Sargassum in the tropical AtlanticAIP Advances, Vol. 12, No. 10 | 10 October 2022
- tgEDMD: Approximation of the Kolmogorov Operator in Tensor Train FormatJournal of Nonlinear Science, Vol. 32, No. 4 | 9 May 2022
- Generative Stochastic Modeling of Strongly Nonlinear Flows with Non-Gaussian StatisticsSIAM/ASA Journal on Uncertainty Quantification, Vol. 10, No. 2 | 29 June 2022
- Open-flow mixing and transfer operatorsPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 380, No. 2225 | 25 April 2022
- Modern Koopman Theory for Dynamical SystemsSIAM Review, Vol. 64, No. 2 | 5 May 2022
- Embedding classical dynamics in a quantum computerPhysical Review A, Vol. 105, No. 5 | 3 May 2022
- Deep Lagrangian Connectivity in the Global Ocean Inferred from Argo FloatsJournal of Physical Oceanography, Vol. 52, No. 5 | 1 May 2022
- Learning and Leveraging Features in Flow-Like Environments to Improve Situational AwarenessIEEE Robotics and Automation Letters, Vol. 7, No. 2 | 1 Apr 2022
- Approximative Policy Iteration for Exit Time Feedback Control Problems Driven by Stochastic Differential Equations using Tensor Train FormatMultiscale Modeling & Simulation, Vol. 20, No. 1 | 21 March 2022
- Decomposing the dynamics of the Lorenz 1963 model using unstable periodic orbits: Averages, transitions, and quasi-invariant setsChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 32, No. 3 | 23 March 2022
- Ensemble Forecasts in Reproducing Kernel Hilbert Space Manifold: Dynamical Systems in WonderlandSSRN Electronic Journal, Vol. 2 | 1 Jan 2022
- Tensor-based computation of metastable and coherent setsPhysica D: Nonlinear Phenomena, Vol. 427 | 1 Dec 2021
- Spectral analysis of climate dynamics with operator-theoretic approachesNature Communications, Vol. 12, No. 1 | 12 November 2021
- Verifying Stochastic Hybrid Systems with Temporal Logic Specifications via Model ReductionACM Transactions on Embedded Computing Systems, Vol. 20, No. 6 | 15 November 2021
- Dynamical integrity assessment of stable equilibria: a new rapid iterative procedureNonlinear Dynamics, Vol. 106, No. 3 | 18 October 2021
- Reproducing kernel Hilbert space compactification of unitary evolution groupsApplied and Computational Harmonic Analysis, Vol. 54 | 1 Sep 2021
- Eigenfunctions of the Perron–Frobenius operator and the finite-time Lyapunov exponents in uniformly hyperbolic area-preserving mapsJournal of Physics A: Mathematical and Theoretical, Vol. 54, No. 28 | 11 June 2021
- A data-driven method for computing polyhedral invariant sets of black-box switched linear systems2021 American Control Conference (ACC) | 25 May 2021
- Koopman Operators for Estimation and Control of Dynamical SystemsAnnual Review of Control, Robotics, and Autonomous Systems, Vol. 4, No. 1 | 3 May 2021
- How can we describe density evolution under delayed dynamics?Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 31, No. 4 | 12 April 2021
- Efficient Numerical Evaluation of Thermodynamic Quantities on Infinite (Semi-)classical ChainsJournal of Statistical Physics, Vol. 182, No. 3 | 6 March 2021
- Cell-mapping orbit search for mission design at ocean worlds using parallel computingThe Journal of the Astronautical Sciences, Vol. 68, No. 1 | 31 March 2021
- Delay-coordinate maps, coherence, and approximate spectra of evolution operatorsResearch in the Mathematical Sciences, Vol. 8, No. 1 | 28 January 2021
- Transition paths of marine debris and the stability of the garbage patchesChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 31, No. 3 | 2 March 2021
- A probabilistic algorithm for aggregating vastly undersampled large Markov chainsPhysica D: Nonlinear Phenomena, Vol. 416 | 1 Feb 2021
- Spectral Properties of Effective Dynamics from Conditional ExpectationsEntropy, Vol. 23, No. 2 | 21 January 2021
- Spectral Early-Warning Signals for Sudden Changes in Time-Dependent Flow PatternsFluids, Vol. 6, No. 2 | 22 January 2021
- On the Approximation of Koopman Spectra of Measure-Preserving FlowsSIAM Journal on Applied Dynamical Systems, Vol. 20, No. 1 | 4 February 2021
- Kernel Analog Forecasting: Multiscale Test ProblemsMultiscale Modeling & Simulation, Vol. 19, No. 2 | 16 June 2021
- Dimension Estimates for Dynamical Systems with Some Degree of Non-injectivity and NonsmoothnessAttractor Dimension Estimates for Dynamical Systems: Theory and Computation | 2 July 2020
- Scenario-Based Set Invariance Verification for Black-Box Nonlinear SystemsIEEE Control Systems Letters, Vol. 5, No. 1 | 1 Jan 2021
- Systemic Risk, Financial Stability and the Choice between a Merger/Acquisition and a Strategic- Alliance/Joint-Venture.SSRN Electronic Journal, Vol. 4 | 1 Jan 2021
- Data-driven Koopman operator approach for computational neuroscienceAnnals of Mathematics and Artificial Intelligence, Vol. 88, No. 11-12 | 11 November 2019
- Computationally Efficient Learning of Large Scale Dynamical Systems: A Koopman Theoretic Approach2020 IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm) | 11 Nov 2020
- Fourier approximation of the statistical properties of Anosov maps on toriNonlinearity, Vol. 33, No. 11 | 8 October 2020
- Transfer operator approach to ray-tracing in circular domainsNonlinearity, Vol. 33, No. 11 | 30 September 2020
- A Dynamic Laplacian for Identifying Lagrangian Coherent Structures on Weighted Riemannian ManifoldsJournal of Nonlinear Science, Vol. 30, No. 5 | 22 June 2017
- On Robust Computation of Koopman Operator and Prediction in Random Dynamical SystemsJournal of Nonlinear Science, Vol. 30, No. 5 | 13 November 2019
- Ensemble-based method for the inverse Frobenius–Perron operator problem: Data-driven global analysis from spatiotemporal “Movie” dataPhysica D: Nonlinear Phenomena, Vol. 411 | 1 Oct 2020
- Koopman spectra in reproducing kernel Hilbert spacesApplied and Computational Harmonic Analysis, Vol. 49, No. 2 | 1 Sep 2020
- Higher-order finite element approximation of the dynamic LaplacianESAIM: Mathematical Modelling and Numerical Analysis, Vol. 54, No. 5 | 28 July 2020
- Data Driven Online Learning of Power System Dynamics2020 IEEE Power & Energy Society General Meeting (PESGM) | 2 Aug 2020
- A Geometric Heat-Flow Theory of Lagrangian Coherent StructuresJournal of Nonlinear Science, Vol. 30, No. 4 | 19 May 2020
- Operator-theoretic framework for forecasting nonlinear time series with kernel analog techniquesPhysica D: Nonlinear Phenomena, Vol. 409 | 1 Aug 2020
- Ruelle–Pollicott Resonances of Stochastic Systems in Reduced State Space. Part III: Application to the Cane–Zebiak Model of the El Niño–Southern OscillationJournal of Statistical Physics, Vol. 179, No. 5-6 | 30 November 2019
- Response and Sensitivity Using Markov ChainsJournal of Statistical Physics, Vol. 179, No. 5-6 | 19 February 2020
- Dynamic mode decomposition for analytic mapsCommunications in Nonlinear Science and Numerical Simulation, Vol. 84 | 1 May 2020
- Diffusion maps embedding and transition matrix analysis of the large-scale flow structure in turbulent Rayleigh–Bénard convectionNonlinearity, Vol. 33, No. 4 | 27 February 2020
- A Set-Oriented Path Following Method for the Approximation of Parameter Dependent AttractorsSIAM Journal on Applied Dynamical Systems, Vol. 19, No. 1 | 31 March 2020
- Data-Driven Approximations of Dynamical Systems Operators for ControlThe Koopman Operator in Systems and Control | 23 February 2020
- Input-Output Networks, Singularity Theory, and HomeostasisAdvances in Dynamics, Optimization and Computation | 21 July 2020
- The Approximation of Invariant Sets in Infinite Dimensional Dynamical SystemsAdvances in Dynamics, Optimization and Computation | 21 July 2020
- Set-Oriented and Finite-Element Study of Coherent Behavior in Rayleigh-Bénard ConvectionAdvances in Dynamics, Optimization and Computation | 21 July 2020
- A Weak Characterization of Slow Variables in Stochastic Dynamical SystemsAdvances in Dynamics, Optimization and Computation | 21 July 2020
- Diffusion maps tailored to arbitrary non-degenerate Itô processesApplied and Computational Harmonic Analysis, Vol. 48, No. 1 | 1 Jan 2020
- Extraction and prediction of coherent patterns in incompressible flows through space–time Koopman analysisPhysica D: Nonlinear Phenomena, Vol. 402 | 1 Jan 2020
- Detecting flow features in scarce trajectory data using networks derived from symbolic itineraries: an application to surface drifters in the North AtlanticNonlinear Processes in Geophysics, Vol. 27, No. 4 | 14 November 2020
- Stability of the Malvinas CurrentChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 30, No. 1 | 30 January 2020
- Koopman Operator Methods for Global Phase Space Exploration of Equivariant Dynamical SystemsIFAC-PapersOnLine, Vol. 53, No. 2 | 1 Jan 2020
- On maximizing the positive Lyapunov exponent of chaotic oscillators applying DE and PSOInternational Journal of Dynamics and Control, Vol. 7, No. 4 | 10 September 2019
- Markov modeling via ordinal partitions: An alternative paradigm for network-based time-series analysisPhysical Review E, Vol. 100, No. 6 | 18 December 2019
- On Information Transfer in Dynamical Systems with applications in Control of Non-equilibrium Dynamics2019 Sixth Indian Control Conference (ICC) | 1 Dec 2019
- Lagrangian coherent sets in turbulent Rayleigh-Bénard convectionPhysical Review E, Vol. 100, No. 5 | 11 November 2019
- Lagrangian perspectives on turbulent superstructures in Rayleigh‐Bénard convectionPAMM, Vol. 19, No. 1 | 18 November 2019
- Spatiotemporal Pattern Extraction by Spectral Analysis of Vector-Valued ObservablesJournal of Nonlinear Science, Vol. 29, No. 5 | 13 May 2019
- Sparse eigenbasis approximation: Multiple feature extraction across spatiotemporal scales with application to coherent set identificationCommunications in Nonlinear Science and Numerical Simulation, Vol. 77 | 1 Oct 2019
- Quenched stochastic stability for eventually expanding-on-average random interval map cocyclesErgodic Theory and Dynamical Systems, Vol. 39, No. 10 | 25 January 2018
- Stability and Approximation of Statistical Limit Laws for Multidimensional Piecewise Expanding MapsAnnales Henri Poincaré, Vol. 20, No. 9 | 13 July 2019
- Data-driven spectral decomposition and forecasting of ergodic dynamical systemsApplied and Computational Harmonic Analysis, Vol. 47, No. 2 | 1 Sep 2019
- Quantum mechanics and data assimilationPhysical Review E, Vol. 100, No. 3 | 9 September 2019
- Stochastic basins of attraction and generalized committor functionsPhysical Review E, Vol. 100, No. 2 | 19 August 2019
- Coarse-graining molecular systems by spectral matchingThe Journal of Chemical Physics, Vol. 151, No. 4 | 30 July 2019
- Delay-Coordinate Maps and the Spectra of Koopman OperatorsJournal of Statistical Physics, Vol. 175, No. 6 | 2 April 2019
- Provably convergent implementations of the subdivision algorithm for the computation of invariant objectsNumerische Mathematik, Vol. 142, No. 1 | 10 October 2018
- Markov-chain-inspired search for MH370Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 29, No. 4 | 30 April 2019
- Simultaneous coherent structure coloring facilitates interpretable clustering of scientific data by amplifying dissimilarityPLOS ONE, Vol. 14, No. 3 | 13 March 2019
- On the Approximation of Koopman Spectra for Measure Preserving TransformationsSIAM Journal on Applied Dynamical Systems, Vol. 18, No. 3 | 13 August 2019
- The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding TechniquesSIAM Journal on Applied Dynamical Systems, Vol. 18, No. 3 | 2 July 2019
- Reasoning, Knowledge Representation and Algorithmic Turning-Point Problems Given Anomalies Inherent in DERs and ASRsComplex Systems, Multi-Sided Incentives and Risk Perception in Companies | 7 September 2019
- Complexity and Some Numerical Algorithmic Turning-Point Problems Inherent in Excessive Outstanding SharesComplex Systems, Multi-Sided Incentives and Risk Perception in Companies | 7 September 2019
- Knowledge-Representation, Belief Systems and an Index of the Seller’s Propensity-To-Sell Real EstateComplex Systems, Multi-Sided Incentives and Risk Perception in Companies | 7 September 2019
- Knowledge-Representation and Network Decisions in Franchising and Online-Retailing Under Combined MN-Transferable-Utility, WTAL, Perception and Regret-Minimization RegimesComplex Systems, Multi-Sided Incentives and Risk Perception in Companies | 7 September 2019
- On Franchise Royalty Rates, Franchise Fees and Incentive EffectsComplex Systems, Multi-Sided Incentives and Risk Perception in Companies | 7 September 2019
- Lagrangian Geography of the Deep Gulf of MexicoJournal of Physical Oceanography, Vol. 49, No. 1 | 1 Jan 2019
- From metastable to coherent sets— Time-discretization schemesChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 29, No. 1 | 28 January 2019
- A kernel-based approach to molecular conformation analysisThe Journal of Chemical Physics, Vol. 149, No. 24 | 27 December 2018
- On sample-based computations of invariant setsNonlinear Dynamics, Vol. 94, No. 4 | 13 August 2018
- A scalable approach to the computation of invariant measures for high-dimensional Markovian systemsScientific Reports, Vol. 8, No. 1 | 29 January 2018
- From Large Deviations to Semidistances of Transport and Mixing: Coherence Analysis for Finite Lagrangian DataJournal of Nonlinear Science, Vol. 28, No. 5 | 1 June 2018
- Koopman analysis of the long-term evolution in a turbulent convection cellJournal of Fluid Mechanics, Vol. 847 | 29 May 2018
- Data-driven spectral decomposition of ECoG signal from an auditory oddball experiment in a marmoset monkey: Implications for EEG data in humans2018 International Joint Conference on Neural Networks (IJCNN) | 1 Jul 2018
- Data-Driven Model Reduction and Transfer Operator ApproximationJournal of Nonlinear Science, Vol. 28, No. 3 | 3 January 2018
- Optimal perturbations for nonlinear systems using graph-based optimal transportCommunications in Nonlinear Science and Numerical Simulation, Vol. 59 | 1 Jun 2018
- Robust Approximation of Koopman Operator and Prediction in Random Dynamical Systems2018 Annual American Control Conference (ACC) | 1 Jun 2018
- Data-Driven Approximation of Transfer Operators: Naturally Structured Dynamic Mode Decomposition2018 Annual American Control Conference (ACC) | 1 Jun 2018
- Crisis of the chaotic attractor of a climate model: a transfer operator approachNonlinearity, Vol. 31, No. 5 | 10 April 2018
- An extended transfer operator approach to identify separatrices in open flowsChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 28, No. 5 | 1 May 2018
- Transition Manifolds of Complex Metastable SystemsJournal of Nonlinear Science, Vol. 28, No. 2 | 12 October 2017
- Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical SystemsJournal of Statistical Physics, Vol. 170, No. 6 | 19 February 2018
- A rigorous computational approach to linear responseNonlinearity, Vol. 31, No. 3 | 12 February 2018
- Periodic Orbit-Attitude Solutions in the Planar Elliptic Restricted Three-Body ProblemJournal of Guidance, Control, and Dynamics, Vol. 41, No. 3 | 1 Mar 2018
- Optimal Data-Driven Estimation of Generalized Markov State Models for Non-Equilibrium DynamicsComputation, Vol. 6, No. 1 | 26 February 2018
- Resonances in a Chaotic Attractor Crisis of the Lorenz FlowJournal of Statistical Physics, Vol. 170, No. 3 | 7 December 2017
- Mixed-Integer Programming for Cycle Detection in Nonreversible Markov ProcessesMultiscale Modeling & Simulation, Vol. 16, No. 1 | 15 February 2018
- Robust FEM-Based Extraction of Finite-Time Coherent Sets Using Scattered, Sparse, and Incomplete TrajectoriesSIAM Journal on Applied Dynamical Systems, Vol. 17, No. 2 | 28 June 2018
- Contracting and Optimal Rents in Commercial Real Estate LeasingSSRN Electronic Journal, Vol. 26 | 1 Jan 2018
- Lagrangian dynamical geography of the Gulf of MexicoScientific Reports, Vol. 7, No. 1 | 1 August 2017
- A coherent structure approach for parameter estimation in Lagrangian Data AssimilationPhysica D: Nonlinear Phenomena, Vol. 360 | 1 Dec 2017
- Frontiers of chaotic advectionReviews of Modern Physics, Vol. 89, No. 2 | 14 June 2017
- Efficient simulation of threshold behaviorArtificial Intelligence for Engineering Design, Analysis and Manufacturing, Vol. 31, No. 2 | 4 May 2017
- Optimal initial condition of passive tracers for their maximal mixing in finite timePhysical Review Fluids, Vol. 2, No. 5 | 1 May 2017
- A critical comparison of Lagrangian methods for coherent structure detectionChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 27, No. 5 | 4 May 2017
- Understanding the geometry of transport: Diffusion maps for Lagrangian trajectory data unravel coherent setsChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 27, No. 3 | 22 February 2017
- Contaminant transport at large Courant numbers using Markov matricesBuilding and Environment, Vol. 112 | 1 Feb 2017
- A Set-Oriented Numerical Approach for Dynamical Systems with Parameter UncertaintySIAM Journal on Applied Dynamical Systems, Vol. 16, No. 1 | 12 January 2017
- Optimal Mixing EnhancementSIAM Journal on Applied Mathematics, Vol. 77, No. 4 | 24 August 2017
- Transfer Operator-Based Extraction of Coherent Features on SurfacesTopological Methods in Data Analysis and Visualization IV | 3 June 2017
- Using Dynamics to Analyse Time SeriesPatterns of Dynamics | 8 February 2018
- Computing coherent sets using the Fokker-Planck equationJournal of Computational Dynamics, Vol. 3, No. 2 | 1 Dec 2016
- Towards tensor-based methods for the numerical approximation of the Perron--Frobenius and Koopman operatorJournal of Computational Dynamics, Vol. 3, No. 2 | 1 Nov 2016
- ReferencesIllegal Online File Sharing, Decision-Analysis, and the Pricing of Digital Goods | 1 November 2016
- On the computation of attractors for delay differential equationsJournal of Computational Dynamics, Vol. 3, No. 1 | 1 Oct 2016
- Periodic Orbit-Attitude Solutions in the Planar Elliptic Restricted Three-Body ProblemAIAA/AAS Astrodynamics Specialist Conference | 9 September 2016
- Cheeger inequalities for absorbing Markov chainsAdvances in Applied Probability, Vol. 48, No. 3 | 19 September 2016
- On the numerical approximation of the Perron-Frobenius and Koopman operatorJournal of Computational Dynamics, Vol. 3, No. 1 | 1 Sep 2016
- A trajectory-free framework for analysing multiscale systemsPhysica D: Nonlinear Phenomena, Vol. 328-329 | 1 Aug 2016
- Spectral-clustering approach to Lagrangian vortex detectionPhysical Review E, Vol. 93, No. 6 | 17 June 2016
- A dynamical systems model of price bubbles and cyclesQuantitative Finance, Vol. 16, No. 2 | 1 February 2016
- Optimal Mixing Enhancement by Local PerturbationSIAM Review, Vol. 58, No. 3 | 4 August 2016
- Response Operators for Markov Processes in a Finite State Space: Radius of Convergence and Link to the Response Theory for Axiom A SystemsJournal of Statistical Physics, Vol. 162, No. 2 | 7 December 2015
- A numerical framework to understand transitions in high-dimensional stochastic dynamical systemsDynamics and Statistics of the Climate System, Vol. 1, No. 1 | 30 November 2016
- Mesochronic classification of trajectories in incompressible 3D vector fields over finite timesDiscrete & Continuous Dynamical Systems - S, Vol. 9, No. 4 | 1 Jan 2016
- Constructing Markov matrices for real-time transient contaminant transport analysis for indoor environmentsBuilding and Environment, Vol. 94 | 1 Dec 2015
- Computation of the Lyapunov measure for almost everywhere stochastic stability2015 54th IEEE Conference on Decision and Control (CDC) | 1 Dec 2015
- A new network approach to Bayesian inference in partial differential equationsInternational Journal for Numerical Methods in Engineering, Vol. 104, No. 5 | 26 May 2015
- Stochastic Stability of Lyapunov Exponents and Oseledets Splittings for Semi‐invertible Matrix CocyclesCommunications on Pure and Applied Mathematics, Vol. 68, No. 11 | 9 March 2015
- Role of critical points of the skin friction field in formation of plumes in thermal convectionPhysical Review E, Vol. 92, No. 4 | 6 October 2015
- Cellular non-deterministic automata and partial differential equationsPhysica D: Nonlinear Phenomena, Vol. 311-312 | 1 Sep 2015
- Pseudo generators for under-resolved molecular dynamicsThe European Physical Journal Special Topics, Vol. 224, No. 12 | 22 June 2015
- Thirty years of turnstiles and transportChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 25, No. 9 | 23 March 2015
- Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic setsChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 25, No. 5 | 6 May 2015
- Statistical verification of dynamical systems using set oriented methodsProceedings of the 18th International Conference on Hybrid Systems: Computation and Control | 14 April 2015
- An early warning indicator for atmospheric blocking events using transfer operatorsChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 25, No. 3 | 18 February 2015
- Gaussian Markov transition models of molecular kineticsThe Journal of Chemical Physics, Vol. 142, No. 8 | 24 February 2015
- Pseudogenerators of Spatial Transfer OperatorsSIAM Journal on Applied Dynamical Systems, Vol. 14, No. 3 | 1 September 2015
- New Lagrangian diagnostics for characterizing fluid flow mixingPhysics of Fluids, Vol. 26, No. 12 | 15 December 2014
- How well-connected is the surface of the global ocean?Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 24, No. 3 | 1 Sep 2014
- A semi-invertible operator Oseledets theoremErgodic Theory and Dynamical Systems, Vol. 34, No. 4 | 11 March 2013
- Computing the invariant measure and the Lyapunov exponent for one-dimensional maps using a measure-preserving polynomial basisMathematics of Computation, Vol. 83, No. 288 | 12 November 2013
- Probability, statistics and computation in dynamical systemsMathematical Structures in Computer Science, Vol. 24, No. 3 | 28 March 2014
- Rough parameter dependence in climate models and the role of Ruelle-Pollicott resonancesProceedings of the National Academy of Sciences, Vol. 111, No. 5 | 17 January 2014
- Cellular Probabilistic Automata---A Novel Method for Uncertainty PropagationSIAM/ASA Journal on Uncertainty Quantification, Vol. 2, No. 1 | 4 February 2014
- An Elementary Approach to Rigorous Approximation of Invariant MeasuresSIAM Journal on Applied Dynamical Systems, Vol. 13, No. 2 | 10 June 2014
- A Computational Method to Extract Macroscopic Variables and Their Dynamics in Multiscale SystemsSIAM Journal on Applied Dynamical Systems, Vol. 13, No. 4 | 10 December 2014
- Absolute flux optimising curves of flows on a surfaceJournal of Mathematical Analysis and Applications, Vol. 409, No. 1 | 1 Jan 2014
- A closing scheme for finding almost-invariant sets in open dynamical systemsJournal of Computational Dynamics, Vol. 1, No. 1 | 1 Jan 2014
- Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic toolsJournal of Computational Dynamics, Vol. 1, No. 2 | 1 Jan 2014
- The computation of convex invariant sets via Newton's methodJournal of Computational Dynamics, Vol. 1, No. 1 | 1 Jan 2014
- Toward the Extraction of Saddle Periodic OrbitsTopological Methods in Data Analysis and Visualization III | 19 March 2014
- Almost-Invariant and Finite-Time Coherent Sets: Directionality, Duration, and DiffusionErgodic Theory, Open Dynamics, and Coherent Structures | 12 April 2014
- METASTABILITY, LYAPUNOV EXPONENTS, ESCAPE RATES, AND TOPOLOGICAL ENTROPY IN RANDOM DYNAMICAL SYSTEMSStochastics and Dynamics, Vol. 13, No. 04 | 7 October 2013
- Adaptive spectral clustering with application to tripeptide conformation analysisThe Journal of Chemical Physics, Vol. 139, No. 19 | 20 November 2013
- Mapping the dynamic repertoire of the resting brainNeuroImage, Vol. 78 | 1 Sep 2013
- Copulas related to Manneville–Pomeau processesBrazilian Journal of Probability and Statistics, Vol. 27, No. 3 | 1 Aug 2013
- Fuzzy spectral clustering by PCCA+: application to Markov state models and data classificationAdvances in Data Analysis and Classification, Vol. 7, No. 2 | 31 May 2013
- A set oriented definition of finite-time Lyapunov exponents and coherent setsCommunications in Nonlinear Science and Numerical Simulation, Vol. 18, No. 5 | 1 May 2013
- An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systemsPhysica D: Nonlinear Phenomena, Vol. 250 | 1 May 2013
- Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: A comparative numerical studyPhysica D: Nonlinear Phenomena, Vol. 247, No. 1 | 1 Mar 2013
- Estimating Long-Term Behavior of Flows without Trajectory Integration: The Infinitesimal Generator ApproachSIAM Journal on Numerical Analysis, Vol. 51, No. 1 | 24 January 2013
- Conditionally Stationary Measures for Random DiffeomorphismsProcedia IUTAM, Vol. 6 | 1 Jan 2013
- On the mixing properties of piecewise expanding maps under composition with permutationsDiscrete and Continuous Dynamical Systems, Vol. 33, No. 8 | 1 Jan 2013
- Analysis of Streamline Separation at Infinity Using Time-Discrete Markov ChainsIEEE Transactions on Visualization and Computer Graphics, Vol. 18, No. 12 | 1 Dec 2012
- Applied KoopmanismChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 22, No. 4 | 21 December 2012
- Topological chaos, braiding and bifurcation of almost-cyclic setsChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 22, No. 4 | 6 December 2012
- Geometric ergodicity and the spectral gap of non-reversible Markov chainsProbability Theory and Related Fields, Vol. 154, No. 1-2 | 3 June 2011
- Efficient optimal design of uncertain discrete time dynamical systemsAutomatica, Vol. 48, No. 10 | 1 Oct 2012
- Finite-time entropy: A probabilistic approach for measuring nonlinear stretchingPhysica D: Nonlinear Phenomena, Vol. 241, No. 19 | 1 Oct 2012
- Long‐time behavior of the proper orthogonal decomposition methodNumerical Linear Algebra with Applications, Vol. 19, No. 5 | 26 January 2012
- Stabilization of nonlinear systems over packet-drop links: Scalar caseSystems & Control Letters, Vol. 61, No. 9 | 1 Sep 2012
- Traffic modelling framework for electric vehiclesInternational Journal of Control, Vol. 85, No. 7 | 1 Jul 2012
- Invariant Density Analysis: Modeling and Analysis of the Postural Control System Using Markov ChainsIEEE Transactions on Biomedical Engineering, Vol. 59, No. 4 | 1 Apr 2012
- Detecting and Exploiting Chaotic Transport in Mechanical SystemsApplications of Chaos and Nonlinear Dynamics in Science and Engineering - Vol. 2 | 24 May 2012
- Reconstitution of Potential Function by Power Spectra of Trajectories in Nonlinear Dynamical SystemsIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E95-A, No. 2 | 1 Jan 2012
- Analysis of persistent nonstationary time series and applicationsCommunications in Applied Mathematics and Computational Science, Vol. 7, No. 2 | 16 October 2012
- The efficient approximation of coherent pairs in non-autonomous dynamical systemsDiscrete & Continuous Dynamical Systems - A, Vol. 32, No. 9 | 1 Jan 2012
- Construction of a finite-time Lyapunov function by meshless collocationDiscrete & Continuous Dynamical Systems - B, Vol. 17, No. 7 | 1 Jan 2012
- Statistical properties of dynamical systems – Simulation and abstract computationChaos, Solitons & Fractals, Vol. 362 | 1 Nov 2011
- Stochastic climate dynamics: Random attractors and time-dependent invariant measuresPhysica D: Nonlinear Phenomena, Vol. 240, No. 21 | 1 Oct 2011
- Spectral degeneracy and escape dynamics for intermittent maps with a holeNonlinearity, Vol. 24, No. 9 | 14 July 2011
- Generalized Sampling-Based Motion PlannersIEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), Vol. 41, No. 3 | 1 Jun 2011
- A Google-like model of road network dynamics and its application to regulation and controlInternational Journal of Control, Vol. 84, No. 3 | 1 Mar 2011
- Hopping over a heat barrierPhysical Review E, Vol. 83, No. 3 | 28 March 2011
- Topological Chaos and Periodic Braiding of Almost-Cyclic SetsPhysical Review Letters, Vol. 106, No. 11 | 18 March 2011
- Markov Chain Based Emissions Models: A Precursor for Green ControlGreen IT: Technologies and Applications | 1 Jan 2011
- Continuous and Discrete Concepts for Detecting Transport Barriers in the Planar Circular Restricted Three Body ProblemNonlinear Science and Complexity | 1 Jan 2011
- Exploring the qualitative behavior of uncertain dynamical systemsNonlinear Dynamics, Vol. 63, No. 1-2 | 5 September 2010
- Wasserstein distances in the analysis of time series and dynamical systemsPhysica D: Nonlinear Phenomena, Vol. 240, No. 1 | 1 Jan 2011
- Perturbation series for calculation of invariant surface splitting in volume-preserving mapsChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 20, No. 4 | 2 November 2010
- Transport in time-dependent dynamical systems: Finite-time coherent setsChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 20, No. 4 | 11 November 2010
- Optimally coherent sets in geophysical flows: A transfer-operator approach to delimiting the stratospheric polar vortexPhysical Review E, Vol. 82, No. 5 | 12 November 2010
- Stability in the almost everywhere sense: A linear transfer operator approachJournal of Mathematical Analysis and Applications, Vol. 368, No. 1 | 1 Aug 2010
- Coherent sets for nonautonomous dynamical systemsPhysica D: Nonlinear Phenomena, Vol. 239, No. 16 | 1 Aug 2010
- Symbolic images and invariant measures of dynamical systemsErgodic Theory and Dynamical Systems, Vol. 30, No. 4 | 17 July 2009
- Coherent structures and isolated spectrum for Perron–Frobenius cocyclesErgodic Theory and Dynamical Systems, Vol. 30, No. 3 | 4 September 2009
- Nonlinear Stabilization via Control Lyapunov MeasureIEEE Transactions on Automatic Control, Vol. 55, No. 6 | 1 Jun 2010
- Flows on graphs and dynamical systemsDifferential Equations and Dynamical Systems, Vol. 18, No. 1-2 | 26 April 2010
- On the Choice between a Sale-Leaseback and DebtSSRN Electronic Journal, Vol. 141 | 1 Jan 2010
- Local expansion concepts for detecting transport barriers in dynamical systemsCommunications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 12 | 1 Dec 2009
- Transfer operator method for control in fluid flowsProceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference | 1 Dec 2009
- An approximate parametrization of the ergodic partition using time averaged observablesProceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference | 1 Dec 2009
- AN EFFICIENT AND ACCURATE METHOD FOR THE ESTIMATION OF ENTROPY AND OTHER DYNAMICAL INVARIANTS FOR PIECEWISE AFFINE CHAOTIC MAPSInternational Journal of Bifurcation and Chaos, Vol. 19, No. 12 | 20 November 2011
- A hybrid method for computing Lyapunov exponentsNumerische Mathematik, Vol. 113, No. 3 | 29 May 2009
- Almost-invariant sets and invariant manifolds — Connecting probabilistic and geometric descriptions of coherent structures in flowsPhysica D: Nonlinear Phenomena, Vol. 238, No. 16 | 1 Aug 2009
- Towards effective dynamics in complex systems by Markov kernel approximationESAIM: Mathematical Modelling and Numerical Analysis, Vol. 43, No. 4 | 8 July 2009
- On the Approximation of Transport Phenomena - a Dynamical Systems ApproachGAMM-Mitteilungen, Vol. 32, No. 1 | 1 Jun 2009
- Rare Events, Escape Rates and Quasistationarity: Some Exact FormulaeJournal of Statistical Physics, Vol. 135, No. 3 | 29 April 2009
- Invariant Measures of Tunable Chaotic Sources: Robustness Analysis and Efficient EstimationIEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 56, No. 4 | 1 Apr 2009
- A decomposed equation for local entropy and entropy production in volume-preserving coarse-grained systemsPhysica A: Statistical Mechanics and its Applications, Vol. 388, No. 4 | 1 Feb 2009
- Discretization of the Frobenius–Perron Operator Using a Sparse Haar Tensor Basis: The Sparse Ulam MethodSIAM Journal on Numerical Analysis, Vol. 47, No. 5 | 29 October 2009
- Mean Field Approximation in Conformation DynamicsMultiscale Modeling & Simulation, Vol. 8, No. 1 | 25 November 2009
- Computation of uncertainty distributions in complex dynamical systems2009 American Control Conference | 1 Jan 2009
- A non-equilibrium analysis and control framework for active queue managementAutomatica, Vol. 44, No. 10 | 1 Oct 2008
- Optimal partition and effective dynamics of complex networksProceedings of the National Academy of Sciences, Vol. 105, No. 23 | 10 June 2008
- Towards hybrid system modeling of uncertain complex dynamical systemsNonlinear Analysis: Hybrid Systems, Vol. 2, No. 2 | 1 Jun 2008
- An approach for nonlinear model extraction from time-series data2008 American Control Conference | 1 Jun 2008
- Identifying almost invariant sets in stochastic dynamical systemsChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 18, No. 2 | 18 June 2008
- Unwrapping eigenfunctions to discover the geometry of almost-invariant sets in hyperbolic mapsPhysica D: Nonlinear Phenomena, Vol. 237, No. 6 | 1 May 2008
- Lyapunov measure and control of periodic orbit2008 IEEE International Conference on Electro/Information Technology | 1 May 2008
- An efficient and accurate method for computing the invariant measure of piecewise affine chaotic maps2008 IEEE International Symposium on Circuits and Systems | 1 May 2008
- Markov Chains, Entropy, and Fundamental Limitations in Nonlinear StabilizationIEEE Transactions on Automatic Control, Vol. 53, No. 3 | 1 Apr 2008
- Regular approximations to chaotic mapsChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 18, No. 1 | 10 March 2008
- Lyapunov Measure for Almost Everywhere StabilityIEEE Transactions on Automatic Control, Vol. 53, No. 1 | 1 Feb 2008
- Macroscopic Dynamics of Complex Metastable Systems: Theory, Algorithms, and Application to B-DNASIAM Journal on Applied Dynamical Systems, Vol. 7, No. 2 | 23 May 2008
- Decisions in commercial real estate leasing in the real estate sectorCorporate Ownership and Control, Vol. 5, No. 3 | 1 January 2008
- Litigation decisions in commercial real estate leasingCorporate Ownership and Control, Vol. 5, No. 4 | 1 January 2008
- On the choice between a sale-leaseback and debtCorporate Ownership and Control, Vol. 5, No. 4 | 1 January 2008
- Identification of biomolecular conformations from incomplete torsion angle observations by hidden markov modelsJournal of Computational Chemistry, Vol. 28, No. 15 | 6 August 2007
- Bifurcations of stationary measures of random diffeomorphismsErgodic Theory and Dynamical Systems, Vol. 27, No. 5 | 1 October 2007
- On Set-oriented Numerical Methods for Global Analysis of Non-smooth Mechanical SystemsJournal of Vibration and Control, Vol. 13, No. 9-10 | 19 August 2016
- A posteriori error estimates for Markov approximations of Frobenius–Perron operatorsNonlinear Analysis: Theory, Methods & Applications, Vol. 67, No. 3 | 1 Aug 2007
- Identifying stochastic basin hopping by partitioning with graph modularityPhysica D: Nonlinear Phenomena, Vol. 231, No. 2 | 1 Jul 2007
- The infinitesimal operator for the semigroup of the Frobenius-Perron operator from image sequence data: Vector fields and transport barriers from moviesChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 17, No. 2 | 19 June 2007
- Detection of Coherent Oceanic Structures via Transfer OperatorsPhysical Review Letters, Vol. 98, No. 22 | 30 May 2007
- Some issues in disintermediation and securitizationApplied Mathematics and Computation, Vol. 186, No. 2 | 1 Mar 2007
- Issues in disintermediation in the real estate brokerage sectorApplied Mathematics and Computation, Vol. 186, No. 2 | 1 Mar 2007
- Some game theory and financial contracting issues in corporate transactionsApplied Mathematics and Computation, Vol. 186, No. 2 | 1 Mar 2007
- Observability gramian for nonlinear systems2007 46th IEEE Conference on Decision and Control | 1 Jan 2007
- Site selection in the US retailing industryApplied Mathematics and Computation, Vol. 182, No. 2 | 1 Nov 2006
- Symmetry of attractors and the Perron-Frobenius operatorJournal of Difference Equations and Applications, Vol. 12, No. 11 | 1 Nov 2006
- Model reduction of uncertain complex dynamical systems2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control | 1 Oct 2006
- A Twenty-First Century Guidebook for Applied Dynamical SystemsJournal of Computational and Nonlinear Dynamics, Vol. 1, No. 4 | 19 May 2006
- On target for Venus – set oriented computation of energy efficient low thrust trajectoriesCelestial Mechanics and Dynamical Astronomy, Vol. 95, No. 1-4 | 15 August 2006
- Reduced Stochastic Models for Complex Molecular SystemsComputing and Visualization in Science, Vol. 9, No. 2 | 30 May 2006
- Bayesian State Estimation of Nonlinear Systems Using Approximate Aggregate Markov ChainsIndustrial & Engineering Chemistry Research, Vol. 45, No. 12 | 6 May 2006
- Large deviation asymptotics and control variates for simulating large functionsThe Annals of Applied Probability, Vol. 16, No. 1 | 1 Feb 2006
- Automated Model Reduction for Complex Systems Exhibiting MetastabilityMultiscale Modeling & Simulation, Vol. 5, No. 3 | 26 September 2006
- Locating Closed Hyperstreamlines in Second Order Tensor FieldsVisualization and Processing of Tensor Fields | 1 Jan 2006
- Set Oriented Numerical Methods in Space Mission DesignModern Astrodynamics | 1 Jan 2006
- Graph based multi-scale analysis of building system transport models2006 American Control Conference | 1 Jan 2006
- Control of Non-Equilibrium Dynamics in Communication NetworksProceedings of the 45th IEEE Conference on Decision and Control | 1 Jan 2006
- Contracting and Optimal Rents in Commercial Real Estate Leasing.SSRN Electronic Journal, Vol. 141 | 1 Jan 2006
- Litigation Decisions in Commercial Real Estate LeasingSSRN Electronic Journal, Vol. 21 | 1 Jan 2006
- Return Time Dynamics as a Tool for Finding Almost Invariant SetsAnnals of the New York Academy of Sciences, Vol. 1065, No. 1 | 29 March 2006
- A model for prejudiced learning in noisy environmentsApplied Mathematics and Computation, Vol. 168, No. 1 | 1 Sep 2005
- Spectral Properties of Dynamical Systems, Model Reduction and DecompositionsNonlinear Dynamics, Vol. 41, No. 1-3 | 1 Aug 2005
- Transport of Mars-Crossing Asteroids from the Quasi-Hilda RegionPhysical Review Letters, Vol. 94, No. 23 | 16 June 2005
- TRANSPORT IN DYNAMICAL ASTRONOMY AND MULTIBODY PROBLEMSInternational Journal of Bifurcation and Chaos, Vol. 15, No. 03 | 20 November 2011
- Statistically optimal almost-invariant setsPhysica D: Nonlinear Phenomena, Vol. 200, No. 3-4 | 1 Jan 2005
- Large Deviations Asymptotics and the Spectral Theory of Multiplicatively Regular Markov ProcessesElectronic Journal of Probability, Vol. 10, No. none | 1 Jan 2005
- On Franchise Royalty Rates, Franchise Fees and Incentive EffectsSSRN Electronic Journal, Vol. 32 | 1 Jan 2005
- On the Choice between an M&A Transaction and a Strategic AllianceSSRN Electronic Journal, Vol. 136 | 1 Jan 2005
- Some Issues in Disintermediation and SecuritizationSSRN Electronic Journal, Vol. 26 | 1 Jan 2005
- Decisions in Commercial Real Estate Leasing in Thereal Estate SectorSSRN Electronic Journal, Vol. 141 | 1 Jan 2005
- Issues in Disintermediation in the Real Estate Brokerage Secotr.SSRN Electronic Journal, Vol. 1 | 1 Jan 2005
- Extracting macroscopic dynamics: model problems and algorithmsNonlinearity, Vol. 17, No. 6 | 21 August 2004
- Comparison of systems with complex behaviorPhysica D: Nonlinear Phenomena, Vol. 197, No. 1-2 | 1 Oct 2004
- Approximations of Frobenius–Perron operators via interpolationNonlinear Analysis: Theory, Methods & Applications, Vol. 57, No. 5-6 | 1 May 2004
- An Averaging Principle for Fast Degrees of Freedom Exhibiting Long-Term CorrelationsMultiscale Modeling & Simulation, Vol. 2, No. 3 | 26 July 2006
- IntroductionThe Theory of Chaotic Attractors | 1 Jan 2004
- Uncertainty in the dynamics of conservative maps2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601) | 1 Jan 2004
- Goodwill and Current Costs in Large Corporate TransactionsSSRN Electronic Journal, Vol. 141 | 1 Jan 2004
- Computation of the dominant Lyapunov exponent via spatial integration using matrix normsProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 459, No. 2040 | 8 December 2003
- On the Computation of Invariant Measures in Random Dynamical SystemsStochastics and Dynamics, Vol. 03, No. 02 | 21 November 2011
- Extracting macroscopic stochastic dynamics: Model problemsCommunications on Pure and Applied Mathematics, Vol. 56, No. 2 | 26 November 2002
- Robust Permanence for Ecological Differential Equations, Minimax, and DiscretizationsSIAM Journal on Mathematical Analysis, Vol. 34, No. 5 | 1 August 2006
- Detecting and Locating Near-Optimal Almost-Invariant Sets and CyclesSIAM Journal on Scientific Computing, Vol. 24, No. 6 | 25 July 2006
- Modelling of Quantised Systems by Stochastic AutomataModelling, State Observation and Diagnosis of Quantised Systems | 23 October 2002
- From Molecular Dynamics to Conformation Dynamics in Drug DesignTrends in Nonlinear Analysis | 1 Jan 2003
- Biomolecular conformations can be identified as metastable sets of molecular dynamicsSpecial Volume, Computational Chemistry | 1 Jan 2003
- Congestion and Almost Invariant Sets in Dynamical SystemsSymbolic and Numerical Scientific Computation | 24 June 2003
- Ruelle Perron Frobenius spectrum for Anosov mapsNonlinearity, Vol. 15, No. 6 | 24 September 2002
- Finite approximations of Markov operatorsJournal of Computational and Applied Mathematics, Vol. 147, No. 1 | 1 Oct 2002
- SLYRB measures: natural invariant measures for chaotic systemsPhysica D: Nonlinear Phenomena, Vol. 170, No. 1 | 1 Aug 2002
- “Coarse” stability and bifurcation analysis using stochastic simulators: Kinetic Monte Carlo examplesThe Journal of Chemical Physics, Vol. 116, No. 23 | 15 Jun 2002
- Structure preserving finite element approximations of Markov operatorsNonlinearity, Vol. 15, No. 3 | 18 April 2002
- Phase-Space Transport of Stochastic Chaos in Population Dynamics of Virus SpreadPhysical Review Letters, Vol. 88, No. 23 | 23 May 2002
- SLYRB measures: natural invariant measures for chaotic systemsThe Theory of Chaotic Attractors | 1 Jan 2002
- Hierarchical Uncoupling-Coupling of Metastable ConformationsComputational Methods for Macromolecules: Challenges and Applications | 1 Jan 2002
- Set Oriented Numerical Methods for Dynamical SystemsHandbook of Dynamical Systems | 1 Jan 2002
- ON MARKOV CHAINS AND THE SPECTRA OF THE CORRESPONDING FROBENIUS–PERRON OPERATORSStochastics and Dynamics, Vol. 01, No. 04 | 25 January 2012
- Algorithms for Computing Reachable Sets and Control SetsIFAC Proceedings Volumes, Vol. 34, No. 6 | 1 Jul 2001
- ANIMATION OF CHAOTIC MIXING BY A BACKWARD POINCARE CELL-MAP METHODInternational Journal of Bifurcation and Chaos, Vol. 11, No. 07 | 20 November 2011
- Rigorous numerical investigation of the statistical properties of piecewise expanding maps. A feasibility studyNonlinearity, Vol. 14, No. 3 | 22 March 2001
- Detection and visualization of closed streamlines in planar flowsIEEE Transactions on Visualization and Computer Graphics, Vol. 7, No. 2 | 1 Apr 2001
- Extracting Dynamical Behavior via Markov ModelsNonlinear Dynamics and Statistics | 1 Jan 2001
- Spectrum and Statistical Properties of Chaotic DynamicsEuropean Congress of Mathematics | 1 Jan 2001
- Random Attractors: Robustness, Numerics and Chaotic DynamicsErgodic Theory, Analysis, and Efficient Simulation of Dynamical Systems | 1 Jan 2001
- The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical SystemsErgodic Theory, Analysis, and Efficient Simulation of Dynamical Systems | 1 Jan 2001
- Transfer Operator Approach to Conformational Dynamics in Biomolecular SystemsErgodic Theory, Analysis, and Efficient Simulation of Dynamical Systems | 1 Jan 2001
- On the isolated spectrum of the Perron-Frobenius operatorNonlinearity, Vol. 13, No. 4 | 11 May 2000
- Differential equations in technology and medicine: Computational concepts, adaptive algorithms, and virtual labsComputational Mathematics Driven by Industrial Problems | 28 April 2007
- A Direct Approach to Conformational Dynamics Based on Hybrid Monte CarloJournal of Computational Physics, Vol. 151, No. 1 | 1 May 1999
- Topological Features in Vector FieldsScientific Visualization: The Visual Extraction of Knowledge from Data
- Metastability and Dominant Eigenvalues of Transfer OperatorsNew Algorithms for Macromolecular Simulation
- Multiscale Modelling in Molecular Dynamics: Biomolecular Conformations as Metastable StatesComputer Simulations in Condensed Matter Systems: From Materials to Chemical Biology Volume 1
- Graph Algorithms for Dynamical SystemsAnalysis, Modeling and Simulation of Multiscale Problems
- On target for Venus — set oriented computation of energy efficient low thrust trajectoriesPeriodic, Quasi-Periodic and Chaotic Motions in Celestial Mechanics: Theory and Applications
- Biological systems: Applications and perspectivesAnalysis and Control of Ultrafast Photoinduced Reactions
- Chaos Based Generation of True Random BitsIntelligent Computing Based on Chaos
- The InterPlanetary Superhighway and the Origins ProgramProceedings, IEEE Aerospace Conference
- Computation of control sets using subdivision and continuation techniquesProceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)
- On Stochastic Analysis Approaches for Comparing Complex SystemsProceedings of the 44th IEEE Conference on Decision and Control