A topological classification of locally constant potentials via zero-temperature measures

TL;DR

This paper classifies locally constant functions on subshifts of finite type using zero-temperature measures, linking their distribution to the boundary of generalized rotation sets and exploring entropy regularity.

Contribution

It introduces a topological classification method based on zero-temperature measures and analyzes their relation to rotation sets and entropy boundary regularity.

Findings

Zero-temperature measures are classified topologically.

Distribution of measures relates to boundary of rotation sets.

Entropy function exhibits specific regularity properties on boundaries.

Abstract

We provide a topological classification of locally constant functions over subshifts of finite type via their zero-temperature measures. Our approach is to analyze the relationship between the distribution of the zero-temperature measures and the boundary of higher dimensional generalized rotation sets. We also discuss the regularity of the localized entropy function on the boundary of the generalized rotation sets.