Measures of maximal entropy for non-uniformly hyperbolic maps
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917172512555008 |
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| author | Lima, Yuri Obata, Davi Poletti, Mauricio |
| author_facet | Lima, Yuri Obata, Davi Poletti, Mauricio |
| contents | For $C^{1+}$ maps, possibly non-invertible and with singularities, we prove that each homoclinic class of an ergodic adapted hyperbolic measure carries at most one adapted hyperbolic measure of maximal entropy. We then apply this to study the finiteness/uniqueness of such measures in several different settings: finite horizon dispersing billiards, codimension one partially hyperbolic endomorphisms with ``large'' entropy, robustly non-uniformly hyperbolic volume-preserving endomorphisms as in Andersson-Carrasco-Saghin (2025), and Viana maps (1997). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04676 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Measures of maximal entropy for non-uniformly hyperbolic maps Lima, Yuri Obata, Davi Poletti, Mauricio Dynamical Systems 37B10, 37C05, 37C83, 37C40, 37D25, 37D30, 37D35 For $C^{1+}$ maps, possibly non-invertible and with singularities, we prove that each homoclinic class of an ergodic adapted hyperbolic measure carries at most one adapted hyperbolic measure of maximal entropy. We then apply this to study the finiteness/uniqueness of such measures in several different settings: finite horizon dispersing billiards, codimension one partially hyperbolic endomorphisms with ``large'' entropy, robustly non-uniformly hyperbolic volume-preserving endomorphisms as in Andersson-Carrasco-Saghin (2025), and Viana maps (1997). |
| title | Measures of maximal entropy for non-uniformly hyperbolic maps |
| topic | Dynamical Systems 37B10, 37C05, 37C83, 37C40, 37D25, 37D30, 37D35 |
| url | https://arxiv.org/abs/2405.04676 |