Symbolic dynamics for non-uniformly hyperbolic flows in high dimension
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918139056357376 |
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| author | Lima, Yuri Mongez, Juan Carlos Nascimento, João Paulo |
| author_facet | Lima, Yuri Mongez, Juan Carlos Nascimento, João Paulo |
| contents | 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 exponents outside of $[-χ,χ]$. This extends the recent work of Buzzi, Crovisier, and Lima for three dimensional flows with positive speed. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09050 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symbolic dynamics for non-uniformly hyperbolic flows in high dimension Lima, Yuri Mongez, Juan Carlos Nascimento, João Paulo Dynamical Systems Differential Geometry 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 exponents outside of $[-χ,χ]$. This extends the recent work of Buzzi, Crovisier, and Lima for three dimensional flows with positive speed. 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. |
| title | Symbolic dynamics for non-uniformly hyperbolic flows in high dimension |
| topic | Dynamical Systems Differential Geometry |
| url | https://arxiv.org/abs/2509.09050 |