On the cardinality of measures of maximal relative entropy for smooth skew products
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914162677907456 |
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| author | Castro, Matheus M. Froyland, Gary |
| author_facet | Castro, Matheus M. Froyland, Gary |
| contents | Let $Ω$ and $M$ be compact smooth manifolds and let $Θ:Ω\times M\toΩ\times M$ be a $\mathcal C^{1+α}$ skew-product diffeomorphism over a transitive Anosov base. We show that $Θ$ has at most countably many ergodic hyperbolic measures of maximal relative entropy. When $\dim M=2$, if $Θ$ has positive relative topological entropy, then $Θ$ has at most countably many ergodic measures of maximal relative entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04475 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the cardinality of measures of maximal relative entropy for smooth skew products Castro, Matheus M. Froyland, Gary Dynamical Systems 28D20, 37D25, 37D35, 37H05 Let $Ω$ and $M$ be compact smooth manifolds and let $Θ:Ω\times M\toΩ\times M$ be a $\mathcal C^{1+α}$ skew-product diffeomorphism over a transitive Anosov base. We show that $Θ$ has at most countably many ergodic hyperbolic measures of maximal relative entropy. When $\dim M=2$, if $Θ$ has positive relative topological entropy, then $Θ$ has at most countably many ergodic measures of maximal relative entropy. |
| title | On the cardinality of measures of maximal relative entropy for smooth skew products |
| topic | Dynamical Systems 28D20, 37D25, 37D35, 37H05 |
| url | https://arxiv.org/abs/2510.04475 |