On spatial entropy and periodic entropies of Two-dimensional Shifts of Finite Type

TL;DR

This paper explores the relationship between topological entropy and periodic entropies in two-dimensional shifts of finite type, providing insights into their complexity measures through skew-coordinated systems.

Contribution

It introduces new connections between spatial entropy and periodic entropies using skew-coordinated systems on 2D shifts of finite type.

Findings

Established relationships between topological and periodic entropies

Analyzed the impact of skew-coordinated systems on entropy measures

Enhanced understanding of complexity in 2D shift spaces

Abstract

Topological entropy or spatial entropy is a way to measure the complexity of shift spaces. This study investigates the relationships between the spatial entropy and the various periodic entropies which are computed by skew-coordinated systems $\gamma\in GL_2(\mathbb{Z})$ on two dimensional shifts of finite type.