# Single site factors of Gibbs measures

## TL;DR

This paper demonstrates that classical uniqueness regimes of Gibbs measures, including Bowen, Walters, and H"older classes, are preserved under factor maps between shifts of finite type, given certain mixing conditions.

## Contribution

It extends the understanding of Gibbs measures by showing their classical regimes are closed under factor maps with mixing conditions, beyond H"older continuity.

## Key findings

- Classical uniqueness regimes are closed under factor maps between full shifts.
- Classical regimes are also closed under factors between shifts of finite type with mixing conditions.
- The results generalize the regularity properties of Gibbs measures under factor maps.

## Abstract

It has been an open problem to identify classes of Gibbs measures less regular then H\"older continuous on the full shift which are closed under factor maps. In this article we show that in fact all of the classical uniqueness regimes (Bowen, Walters, and H\"older) from thermodynamic formalism are closed under factor maps between full shifts. In fact we show more generally that the classical uniqueness regimes are closed under factors between shifts of finite type provided the factor map satisfies a suitable mixing in fibers condition.