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Entropies and volume growth of unstable manifolds

Part of: Measure-theoretic ergodic theory Ergodic theory

Published online by Cambridge University Press:  04 February 2021

YUNTAO ZANG
YUNTAO ZANG*
Affiliation:
School of Mathematical Sciences, East China Normal University, Shanghai200062, P.R. China (e-mail: yuntaozang@gmail.com)
*
e-mail: yuntaozang@gmail.com
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Abstract

Let f be a $C^2$ diffeomorphism on a compact manifold. Ledrappier and Young introduced entropies along unstable foliations for an ergodic measure $\mu $ . We relate those entropies to covering numbers in order to give a new upper bound on the metric entropy of $\mu $ in terms of Lyapunov exponents and topological entropy or volume growth of sub-manifolds. We also discuss extensions to the $C^{1+\alpha },\,\alpha>0$ , case.

Keywords

entropyLyapunov exponentsvolume growth

MSC classification

Primary: 37A35: Entropy and other invariants, isomorphism, classification 28D20: Entropy and other invariants
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 4 , April 2022 , pp. 1576 - 1590
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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