Maximal Entropy Measures for Non-Accessible Topological Skew Products
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910398246027264 |
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| author | Tahzibi, Ali Cubas, Richard |
| author_facet | Tahzibi, Ali Cubas, Richard |
| contents | In this paper we establish a dichotomy for the ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms with one-dimensional compact center leaves which are virtually skew products over (transitive) Anosov homeomorphism. We prove that if the whole manifold is the unique minimal invariant set saturated by unstable foliation, then either there exists a unique measure of maximal entropy which is non-hyperbolic or there are exactly two hyperbolic ergodic measures of maximal entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03169 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximal Entropy Measures for Non-Accessible Topological Skew Products Tahzibi, Ali Cubas, Richard Dynamical Systems In this paper we establish a dichotomy for the ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms with one-dimensional compact center leaves which are virtually skew products over (transitive) Anosov homeomorphism. We prove that if the whole manifold is the unique minimal invariant set saturated by unstable foliation, then either there exists a unique measure of maximal entropy which is non-hyperbolic or there are exactly two hyperbolic ergodic measures of maximal entropy. |
| title | Maximal Entropy Measures for Non-Accessible Topological Skew Products |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2404.03169 |