Entropies and volume growth of unstable manifolds

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.

14 pages

Cited by in corpus (2)

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