# Loss of Gibbs property in one-dimensional mixing shifts of finite type

## TL;DR

This paper studies how factor maps from one-dimensional mixing shifts of finite type to sofic shifts can transform Gibbs measures into non-Gibbs measures, revealing conditions under which this loss occurs.

## Contribution

It characterizes when factor maps from mixing shifts of finite type to sofic shifts cause Gibbs measures to become non-Gibbs, highlighting the loss of Gibbs property.

## Key findings

- Identifies conditions leading to loss of Gibbs property under factor maps.
- Provides examples of non-Gibbs measures arising from Gibbs measures.
- Enhances understanding of measure transformations in symbolic dynamics.

## Abstract

Let $\pi$ be a factor map from a one-dimensional mixing shift of finite type $X$ onto a sofic shift $Y$. We investigate when $\pi$ sends Gibbs measures on $X$ to non-Gibbs measures on $Y$.