Existence and Finiteness of equilibrium states for some Partially hyperbolic endomorphisms
Dynamical Systems
2025-07-02 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2504.19312,
title = {Existence and Finiteness of equilibrium states for some Partially hyperbolic endomorphisms},
author = {Alexander Arbieto and Eric Cabezas},
journal= {arXiv preprint arXiv:2504.19312},
year = {2025}
}