On the hybrid control of metric entropy for dominated splittings

Xufeng Guo; Gang Liao; Wenxiang Sun; Dawei Yang

doi:10.3934/dcds.2018219

Article Contents

2018, Volume 38, Issue 10: 5011-5019. Doi: 10.3934/dcds.2018219

This issue Previous Article Selection of calibrated subaction when temperature goes to zero in the discounted problem Next Article Moduli of 3-dimensional diffeomorphisms with saddle-foci

On the hybrid control of metric entropy for dominated splittings

1, 3.
School of Mathematical Sciences, Peking University, Beijing 100871, China
2, 4.
Center for Dynamical Systems and Differential Equations, Soochow University, Suzhou 215006, China

* Author to whom any correspondence should be addressed

Received: September 30, 2017

Revised: April 30, 2018

Published: September 2018

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Abstract

Let $f$ be a $C^1$ diffeomorphism on a compact Riemannian manifold without boundary and $\mu$ an ergodic $f$-invariant measure whose Oseledets splitting admits domination. We give a hybrid estimate from above for the metric entropy of $\mu$ in terms of Lyapunov exponents and volume growth. Furthermore, for any $C^1$ diffeomorphism away from tangencies, its topological entropy is bounded by the volume growth.

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Mathematics Subject Classification: 37D30, 37A35, 37D25.

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References

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