Skip to main navigation Skip to search Skip to main content

SYMBOLIC DYNAMICS FOR NON-UNIFORMLY HYPERBOLIC DIFFEOMORPHISMS OF COMPACT SMOOTH MANIFOLDS

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

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 languageEnglish
Pages (from-to)43-113
Number of pages71
JournalJournal of Modern Dynamics
Volume13
DOIs
StatePublished - 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
©2018 AIMSCIENCES.

Keywords

  • Hyperbolic
  • Lyapunov exponents
  • Markov partition
  • diffeomorphisms
  • manifolds of any dimension
  • non-uniformly hyperbolic
  • symbolic dynamics

Fingerprint

Dive into the research topics of 'SYMBOLIC DYNAMICS FOR NON-UNIFORMLY HYPERBOLIC DIFFEOMORPHISMS OF COMPACT SMOOTH MANIFOLDS'. Together they form a unique fingerprint.

Cite this