(Semi)continuity of the entropy of Sinai probability measures for partially hyperbolic diffeomorphisms

TL;DR

This paper investigates the conditions under which the entropy of Sinai probability measures remains continuous or upper semicontinuous in the context of partially hyperbolic diffeomorphisms, with applications to various examples.

Contribution

It provides new sufficient conditions for the (semi)continuity of Sinai measure entropy in partially hyperbolic systems, expanding understanding of entropy behavior.

Findings

Established conditions for upper semicontinuity of entropy.

Identified criteria for continuity of Sinai measure entropy.

Applied results to multiple examples of partially hyperbolic diffeomorphisms.

Abstract

We establish sufficient conditions for the upper semicontinuity and the continuity of the entropy of Sinai probability measures invariant by partially hyperbolic diffeomorphisms and discuss their application in several examples.