On the number of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms with compact center leaves

2021/06/06 by Rocha, Joas Elias, Tahzibi, Ali · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2106.03116

Abstract

In this paper, we study the number of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms defined on 3-torus with compact center leaves. Assuming the existence of a periodic leaf with Morse-Smale dynamics we prove a sharp upper bound for the number of maximal measures in terms of the number of sources and sinks of Morse-Smale dynamics. A well-known class of examples for which our results apply are the so-called Kan-type diffeomorphisms admitting physical measures with intermingled basins.

Cited by

• Robust Transitivity of Partially Hyperbolic Diffeomorphisms with Interval Central Leaves
• Characterization of Ergodic Measures of Maximal Entropy for Topologically Transitive Partially Hyperbolic Diffeomorphisms with compact center leaves

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