Exponential mixing of measures of maximal entropy for certain skew products
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909859938566144 |
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| author | Marin, Karina Poletti, Mauricio Veiga, Filiphe |
| author_facet | Marin, Karina Poletti, Mauricio Veiga, Filiphe |
| contents | We establish a relation between the continuity of the fiber entropy and the continuity of the fiber Lyapunov exponents for skew products with 2-dimensional fibers. This result extends the theorem for surfaces proved by Buzzi-Crovisier-Sarig. As a consequence, we are able to obtain classes of skew products that satisfies the strong positive recurrence (SPR) property, in particular these maps have finite number of measures of maximal entropy, all exponentially mixing with good statistical properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09908 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponential mixing of measures of maximal entropy for certain skew products Marin, Karina Poletti, Mauricio Veiga, Filiphe Dynamical Systems We establish a relation between the continuity of the fiber entropy and the continuity of the fiber Lyapunov exponents for skew products with 2-dimensional fibers. This result extends the theorem for surfaces proved by Buzzi-Crovisier-Sarig. As a consequence, we are able to obtain classes of skew products that satisfies the strong positive recurrence (SPR) property, in particular these maps have finite number of measures of maximal entropy, all exponentially mixing with good statistical properties. |
| title | Exponential mixing of measures of maximal entropy for certain skew products |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2509.09908 |