Existence and Finiteness of equilibrium states for some Partially hyperbolic endomorphisms
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911031252484096 |
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| author | Arbieto, Alexander Cabezas, Eric |
| author_facet | Arbieto, Alexander Cabezas, Eric |
| contents | We establish the existence and finiteness of equilibrium states for a class of partially hyperbolic endomorphisms. In our first result, we assume that the central direction is simple. In the second result, we consider the case where there exists a dominated splitting along the central direction, which is decomposed into one-dimensional subbundles. This latter result extends the work of C. Alvarez and M. Cantarino \cite{alvarez2022existence} to higher-dimensional central directions. Finally, we demonstrate the finiteness of measures of maximal entropy under the assumption that the central direction is one-dimensional and the integrated Lyapunov exponent is bounded away from zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19312 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and Finiteness of equilibrium states for some Partially hyperbolic endomorphisms Arbieto, Alexander Cabezas, Eric Dynamical Systems We establish the existence and finiteness of equilibrium states for a class of partially hyperbolic endomorphisms. In our first result, we assume that the central direction is simple. In the second result, we consider the case where there exists a dominated splitting along the central direction, which is decomposed into one-dimensional subbundles. This latter result extends the work of C. Alvarez and M. Cantarino \cite{alvarez2022existence} to higher-dimensional central directions. Finally, we demonstrate the finiteness of measures of maximal entropy under the assumption that the central direction is one-dimensional and the integrated Lyapunov exponent is bounded away from zero. |
| title | Existence and Finiteness of equilibrium states for some Partially hyperbolic endomorphisms |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2504.19312 |