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SIAM J. on Applied Dynamical Systems / Volume 11 / Issue 1

SIAM J. Appl. Dyn. Syst. 11, pp. 82-109 (28 pages)

Efficient Automation of Index Pairs in Computational Conley Index Theory

Rafael Frongillo and Rodrigo Treviño

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We present new methods of automating the construction of index pairs, essential ingredients of discrete Conley index theory. These new algorithms are further steps in the direction of automating computer-assisted proofs of semiconjugacies from a map on a manifold to a subshift of finite type. We apply these new algorithms to the standard map at different values of the perturbative parameter $\varepsilon$ and obtain rigorous lower bounds for its topological entropy for $\varepsilon\in[.7,2]$.

© 2012 Society for Industrial and Applied Mathematics

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KEYWORDS

AMS Subject Headings

37M99, 37D99

PUBLICATION DATA

ISSN

1536-0040 (online)

Publisher

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

History
Received September 14, 2010
Accepted November 18, 2011
Published online January 24, 2012
Digital Object Identifier
http://dx.doi.org/10.1137/100808587

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