On the cardinality of measures of maximal relative entropy for smooth skew products

2025/10/06 by Castro, Matheus M., Froyland, Gary
#28D20 #37D25 #37D35 #37H05 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.04475

Abstract

Let Ω and M be compact smooth manifolds and let Θ:Ω× M→Ω× M be a \mathcal C^1+α skew-product diffeomorphism over a transitive Anosov base. We show that Θ has at most countably many ergodic hyperbolic measures of maximal relative entropy. When dim M=2, if Θ has positive relative topological entropy, then Θ has at most countably many ergodic measures of maximal relative entropy.

Related

• Maximal Entropy Measures for Non-Accessible Topological Skew Products
• Finite Measures of Maximal Entropy for an Open Set of Partially Hyperbolic Diffeomorphisms
• Measures of maximal entropy for C^∞ three-dimensional flows
• Partially hyperbolic diffeomorphisims with a finite number of measures of maximal entropy
• Characterization of Ergodic Measures of Maximal Entropy for Topologically Transitive Partially Hyperbolic Diffeomorphisms with compact center leaves