Symbolic dynamics for non-uniformly hyperbolic diffeomorphisms of compact smooth manifolds | Zendy

Snir Ben Ovadia | Zendy

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Symbolic dynamics for non-uniformly hyperbolic diffeomorphisms of compact smooth manifolds

Author(s) -

Snir Ben Ovadia

Publication year - 2018

Publication title -

journal of modern dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.668

H-Index - 25

eISSN - 1930-532X

pISSN - 1930-5311

DOI - 10.3934/jmd.2018013

Subject(s) - mathematics , symbolic dynamics , pure mathematics , bounded function , hyperbolic manifold , topological entropy , countable set , ergodic theory , hyperbolic set , hyperbolic group , hyperbolic equilibrium point , invariant (physics) , uniform boundedness , relatively hyperbolic group , stable manifold , mathematical analysis , entropy (arrow of time) , hyperbolic triangle , hyperbolic function , physics , quantum mechanics , mathematical physics

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.

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