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arXiv · 2307.14319

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

Jérôme Buzzi·Sylvain Crovisier·Yuri Lima
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Abstract

We construct symbolic dynamics for three dimensional flows with positive speed. More precisely, for each $\chi>0$, we code a set of full measure for every invariant probability measure which is $\chi$-hyperbolic. These include all ergodic measures with entropy bigger than $\chi$ as well as all hyperbolic periodic orbits of saddle-type with Lyapunov exponent outside of $[-\chi,\chi]$. 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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Jérôme Buzzi, Sylvain Crovisier, Yuri Lima. 2023-07-26. Symbolic dynamics for large non-uniformly hyperbolic sets of three dimensional flows. https://arxiv.org/abs/2307.14319

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