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

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 symboli...

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Published inErgodic theory and dynamical systems Vol. 41; no. 11; pp. 3244 - 3269
Main Author BEN OVADIA, SNIR
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.11.2021
Subjects
Decomposition
Dynamics
Isomorphism
Orbits
Original Article
37D25
non-uniform hyperbolicity
Markov partition
symbolic dynamics
37B10
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Summary: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].
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2020.114