Symbolic dynamics for large non-uniformly hyperbolic sets of three dimensional flows

2023/07/26 by Buzzi, Jérôme, Crovisier, Sylvain, Lima, Yuri · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.14319

Abstract

We construct symbolic dynamics for three dimensional flows with positive speed. More precisely, for each χ>0, we code a set of full measure for every invariant probability measure which is χ-hyperbolic. These include all ergodic measures with entropy bigger than χ as well as all hyperbolic periodic orbits of saddle-type with Lyapunov exponent outside of [-χ,χ]. This contrasts with a previous work of Lima & Sarig which built a coding associated to a given invariant probability measure. As an application, we code homoclinic classes of measures by suspensions of irreducible countable Markov shifts.

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• Uniqueness of the measure of maximal entropy for geodesic flows on surfaces
• Effective SPR property for surface diffeomorphisms and three-dimensional vector fields

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