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arXiv · 2502.17385

Partially hyperbolic diffeomorphisims with a finite number of measures of maximal entropy

Juan Carlos Mongez·Maria José Pacifico·Mauricio Poletti
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Abstract

We prove the finiteness of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms where the center direction has a dominated decomposition into one dimensional bundle and there is a uniform lower bound for the absolute value of the Lyapunov exponents. As applications we prove finiteness for a class derived from Anosov partially hyperbolic diffeomorphisms defined on $\mathbb{T}^4$ and that in a class of skew product over partially hyperbolic diffeomorphisms there exists a $C^1$ open and $C^r$ dense set of diffeomorphisms with a finite number of ergodic measures of maximal entropy. We also study the upper semicontinuity of the number of measures of maximal entropy with respect to the diffeomorphism.

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Juan Carlos Mongez, Maria José Pacifico, Mauricio Poletti. 2025-02-24. Partially hyperbolic diffeomorphisims with a finite number of measures of maximal entropy. https://arxiv.org/abs/2502.17385

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