Finite Measures of Maximal Entropy for an Open Set of Partially Hyperbolic Diffeomorphisms

2024/01/05 by Juan Carlos Mongez, Mongez, Juan Carlos, Maria José Pacífico +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #Caveolin-1 and cellular processes #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2401.02776

openalex publication_date 2024/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider partially hyperbolic diffeomorphisms f with a one-dimensional central direction such that the unstable entropy exceeds the stable entropy. Our main result proves that such maps have a finite number of ergodic measures of maximal entropy. Moreover, any C¹⁺ diffeomorphism near f in the C¹ topology possesses at most the same number of ergodic measures of maximal entropy. Our contribution is in extending the findings in [4] to arbitrary dimensions. We believe our technique, essentially distinct from the one in that paper, is robust and may find applications in further contexts.

Cited by

• Unique equilibrium states for some partially hyperbolic diffeomorphisms with dominated splittings
• Simple Lyapunov spectrum of partially hyperbolic diffeomorphisms

Related

• Partially hyperbolic diffeomorphisims with a finite number of measures of maximal entropy
• On the number of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms with compact center leaves
• Characterization of Ergodic Measures of Maximal Entropy for Topologically Transitive Partially Hyperbolic Diffeomorphisms with compact center leaves
• Measures of maximal entropy for surface diffeomorphisms
• Maximal Entropy Measures for Non-Accessible Topological Skew Products