Abstract
We construct countable Markov partitions for non-uniformly hyperbolic diffeomorphisms on compact manifolds of any dimension, extending earlier work of Sarig [29] for surfaces. These partitions allow us to obtain symbolic coding on invariant sets of full measure for all hyperbolic measures whose Lyapunov exponents are bounded away from zero by a fixed constant. Applications include counting results for hyperbolic periodic orbits, and structure of hyperbolic measures of maximal entropy.
| Original language | English |
|---|---|
| Pages (from-to) | 43-113 |
| Number of pages | 71 |
| Journal | Journal of Modern Dynamics |
| Volume | 13 |
| DOIs | |
| State | Published - 2018 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:©2018 AIMSCIENCES.
Keywords
- Hyperbolic
- Lyapunov exponents
- Markov partition
- diffeomorphisms
- manifolds of any dimension
- non-uniformly hyperbolic
- symbolic dynamics
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