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A link between topological entropy and Lyapunov exponents

Published online by Cambridge University Press:  20 June 2017

THIAGO CATALAN
THIAGO CATALAN*
Affiliation:
Faculdade de Matemática, FAMAT/UFU, Av. João Naves de Avila, 2121, 38.408-100, Uberlândia, MG, Brazil email tcatalan@ufu.br
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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 $f$ restricted 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.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 3 , March 2019 , pp. 620 - 637
Copyright
© Cambridge University Press, 2017 

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