Symbolic Dynamics for non-uniformly hyperbolic flows in high dimension

Abstract

We construct symbolic dynamics for flows with positive speed in any dimension: for each χ > 0, we code a set that has full measure for every invariant probability measure which is χ–hyperbolic. In particular, the coded set contains all hyperbolic periodic orbits with Lyapunov exponent outside of [ − χ,χ]. This extends the recent work of Buzzi, Crovisier, and Lima for three dimensional flows with positive speed [15]. As an application, we code homoclinic classes of measures by suspensions of irreducible countable Markov shifts, and prove that each such class has at most one probability measure that maximizes the entropy.