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

2025/02/24 by Juan Carlos Mongez, Mongez, Juan Carlos, Maria José Pacífico +3 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Cellular Automata and Applications #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2502.17385

openalex publication_date 2025/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \mathbbT⁴ and that in a class of skew product over partially hyperbolic diffeomorphisms there exists a C¹ 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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• Unique equilibrium states for some partially hyperbolic diffeomorphisms with dominated splittings
• Simple Lyapunov spectrum of partially hyperbolic diffeomorphisms

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