Existence and Finiteness of equilibrium states for some Partially hyperbolic endomorphisms

Fuente: arXiv
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Main Authors: Arbieto, Alexander, Cabezas, Eric
Format: Preprint
Published: 2025
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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