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The set of points with Markovian symbolic dynamics for non-uniformly hyperbolic diffeomorphisms

Part of: Topological dynamics Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  04 November 2020

SNIR BEN OVADIA
SNIR BEN OVADIA*
Affiliation:
Weizmann Institute of Science, Department of Mathematics, Rehovot, 76100, Israel
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Abstract

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The papers [O. M. Sarig. Symbolic dynamics for surface diffeomorphisms with positive entropy. J. Amer. Math. Soc.26(2) (2013), 341–426] and [S. Ben Ovadia. Symbolic dynamics for non-uniformly hyperbolic diffeomorphisms of compact smooth manifolds. J. Mod. Dyn.13 (2018), 43–113] constructed symbolic dynamics for the restriction of $C^r$ diffeomorphisms to a set $M'$ with full measure for all sufficiently hyperbolic ergodic invariant probability measures, but the set $M'$ was not identified there. We improve the construction in a way that enables $M'$ to be identified explicitly. One application is the coding of infinite conservative measures on the homoclinic classes of Rodriguez-Hertz et al. [Uniqueness of SRB measures for transitive diffeomorphisms on surfaces. Comm. Math. Phys.306(1) (2011), 35–49].

Keywords

Markov partitionnon-uniform hyperbolicitysymbolic dynamics

MSC classification

Primary: 37B10: Symbolic dynamics 37D25: Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 11 , November 2021 , pp. 3244 - 3269
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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