Symbolic dynamics for nonuniformly hyperbolic flows in high dimension
Yuri Lima, Juan Carlos Mongez, João Paulo Nascimento
Source abstract
Abstract We construct symbolic dynamics for flows with positive speed in any dimension: for each , we code a set that has full measure for every invariant probability measure that is ‐hyperbolic. In particular, the coded set contains all hyperbolic periodic orbits with Lyapunov exponents outside of . This extends the recent work of Buzzi, Crovisier, and Lima for three‐dimensional flows with positive speed [Buzzi et al., Adv. Math. 479 (2025), 110410]. 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.
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