Partially hyperbolic diffeomorphisims with a finite number of measures of maximal entropy
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912246881320960 |
|---|---|
| author | Mongez, Juan Carlos Pacifico, Maria José Poletti, Mauricio |
| author_facet | Mongez, Juan Carlos Pacifico, Maria José Poletti, Mauricio |
| contents | We prove the finiteness of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms where the center direction has a dominated decomposition into one dimensional bundle and there is a uniform lower bound for the absolute value of the Lyapunov exponents. As applications we prove finiteness for a class derived from Anosov partially hyperbolic diffeomorphisms defined on $\mathbb{T}^4$ and that in a class of skew product over partially hyperbolic diffeomorphisms there exists a $C^1$ open and $C^r$ dense set of diffeomorphisms with a finite number of ergodic measures of maximal entropy. We also study the upper semicontinuity of the number of measures of maximal entropy with respect to the diffeomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17385 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partially hyperbolic diffeomorphisims with a finite number of measures of maximal entropy Mongez, Juan Carlos Pacifico, Maria José Poletti, Mauricio Dynamical Systems We prove the finiteness of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms where the center direction has a dominated decomposition into one dimensional bundle and there is a uniform lower bound for the absolute value of the Lyapunov exponents. As applications we prove finiteness for a class derived from Anosov partially hyperbolic diffeomorphisms defined on $\mathbb{T}^4$ and that in a class of skew product over partially hyperbolic diffeomorphisms there exists a $C^1$ open and $C^r$ dense set of diffeomorphisms with a finite number of ergodic measures of maximal entropy. We also study the upper semicontinuity of the number of measures of maximal entropy with respect to the diffeomorphism. |
| title | Partially hyperbolic diffeomorphisims with a finite number of measures of maximal entropy |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2502.17385 |