Existence and uniqueness of measures of maximal entropy for partially hyperbolic endomorphisms

Carlos F. Álvarez, Marisa Cantarino

Published 2022-07-12Version 1

We prove the existence of measures of maximal entropy for partially hyperbolic endomorphisms with one-dimensional center bundle. We also address the uniqueness of such measures for certain endomorphisms defined on the $n$-torus. More precisely, we obtain a unique measure of maximal entropy -- locally in a $C^1$ neighborhood of a linear Anosov endomorphism, and globally with additional hypotheses.