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

Snir Ben Ovadia

doi:10.1017/etds.2020.114

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

Snir Ben Ovadia^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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 Cr 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].

Original language	English
Pages (from-to)	3244-3269
Number of pages	26
Journal	Ergodic Theory and Dynamical Systems
Volume	41
Issue number	11
DOIs	https://doi.org/10.1017/etds.2020.114
State	Published - 4 Nov 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© The Author(s), 2020. Published by Cambridge University Press.

Keywords

Markov partition
non-uniform hyperbolicity
symbolic dynamics

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10.1017/etds.2020.114

Cite this

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abstract = "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 Cr 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].",

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

Abstract

Bibliographical note

Keywords

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