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The set of points with Markovian symbolic dynamics for non-uniformly hyperbolic diffeomorphisms
- Source :
- Ergodic Theory and Dynamical Systems. 41:3244-3269
- Publication Year :
- 2020
- Publisher :
- Cambridge University Press (CUP), 2020.
-
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 $C^r$ 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].
- Subjects :
- Pure mathematics
Applied Mathematics
General Mathematics
010102 general mathematics
05 social sciences
Symbolic dynamics
01 natural sciences
Measure (mathematics)
0502 economics and business
Markov partition
Ergodic theory
Homoclinic orbit
Uniqueness
0101 mathematics
Invariant (mathematics)
050203 business & management
Mathematics
Probability measure
Subjects
Details
- ISSN :
- 14694417 and 01433857
- Volume :
- 41
- Database :
- OpenAIRE
- Journal :
- Ergodic Theory and Dynamical Systems
- Accession number :
- edsair.doi...........bc064cf085a6dd56508a838ff347a294