Symbolic dynamics for non uniformly hyperbolic diffeomorphisms of compact smooth manifolds
Abstract
We construct countable Markov partitions for non-uniformly hyperbolic diffeomorphisms on compact manifolds of any dimension, extending earlier work of O. Sarig 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 constant. Applications include counting results for hyperbolic periodic orbits, and structure of hyperbolic measures of maximal entropy.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2016
- DOI:
- 10.48550/arXiv.1609.06494
- arXiv:
- arXiv:1609.06494
- Bibcode:
- 2016arXiv160906494B
- Keywords:
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- Mathematics - Dynamical Systems
- E-Print:
- arXiv admin note: substantial text overlap with arXiv:1105.1650 by other authors