Article contents
Entropies and volume growth of unstable manifolds
Published online by Cambridge University Press: 04 February 2021
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.
MSC classification
- Type
- Original Article
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- Copyright
- © The Author(s), 2021. Published by Cambridge University Press
References
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