Zero entropy invariant measures for some skew product diffeomorphisms

TL;DR

This paper investigates skew product diffeomorphisms with nonuniform hyperbolicity, demonstrating the existence of invariant measures with zero entropy and atomic fiber measures, contributing to understanding complex dynamical systems.

Contribution

It introduces the existence of zero entropy invariant measures with atomic fiber measures for certain skew product diffeomorphisms with nonuniform hyperbolicity.

Findings

Existence of zero entropy invariant measures

Atomic conditional measures along fibers

Nonuniform hyperbolic structure analysis

Abstract

In this paper we study some skew product diffeomorphisms with nonuniformly hyperbolic structure along fibers. We show that there is an invariant measure with zero entropy which has atomic conditional measures along fibers.