Sequential Gibbs Measures and Factor Maps

TL;DR

This paper introduces sequential Gibbs measures, extending classical Gibbs measures to non-uniform hyperbolic dynamics, and shows their stability under factor maps with regularity estimates.

Contribution

It defines sequential Gibbs measures and proves their invariance under block factor maps, extending prior results and providing regularity estimates.

Findings

Images of sequential Gibbs measures under factor maps are also sequential Gibbs measures.

The same sequence of Gibbs times is preserved under factor maps.

Regularity estimates of the potential are obtained for the image measure.

Abstract

We define the notion of sequential Gibbs measures, inspired by on the classical notion of Gibbs measures and recent examples from the study of non-uniform hyperbolic dynamics. Extending previous results of Kempton-Pollicott and Ugalde-Chazottes, we show that the images of one block factor maps of a sequential Gibbs measure are also a sequential Gibbs measure, with the same sequence of Gibbs times. We obtain some estimates on the regularity of the potential of the image measure at almost every point.