Characterization of Ergodic Measures of Maximal Entropy for Topologically Transitive Partially Hyperbolic Diffeomorphisms with compact center leaves

TL;DR

This paper investigates the number and support of maximal entropy ergodic measures with zero Lyapunov exponent in certain partially hyperbolic diffeomorphisms on the 3-torus, providing bounds and characterizations.

Contribution

It offers an upper bound on the number of such measures and characterizes their support for topologically transitive partially hyperbolic diffeomorphisms with compact center leaves.

Findings

Bound on the number of maximal entropy ergodic measures with zero Lyapunov exponent.

Characterization of the support of these measures.

Insights into the structure of measures for specific dynamical systems.

Abstract

In this paper, we provide an upper bound on the number of maximal entropy ergodic measures with zero Lyapunov exponent for topologically transitive partially hyperbolic diffeomorphisms with compact one-dimensional center leaves on $\mathbb{T}^3$. Furthermore, we establish a comprehensive characterization of the support of these measures.