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arXiv · 1601.04025

A link between Topological Entropy and Lyapunov Exponents

Thiago Catalan
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Abstract

We show that a $C^1-$generic non partially hyperbolic symplectic diffeomorphism $f$ has topological entropy equal to the supremum of the sum of the positive Lyapunov exponents of its hyperbolic periodic points. Moreover, we also prove that $f$ has topological entropy approximated by the topological entropy of $f$ restrict to basic hyperbolic sets. In particular, the topological entropy map is lower semicontinuous in a $C^1-$generic set of symplectic diffeomorphisms far from partial hyperbolicity.

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Thiago Catalan. 2016-01-15. A link between Topological Entropy and Lyapunov Exponents. https://doi.org/10.1017/etds.2017.39

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