Continuous shift commuting maps between ultragraph shift spaces

TL;DR

This paper characterizes continuous shift-commuting maps between ultragraph shift spaces, extending classical symbolic dynamics results to infinite alphabet cases linked with ultragraph C*-algebras.

Contribution

It proves a Curtis-Hedlund-Lyndon type theorem and characterizes shift-commuting maps via generalized sliding block codes for ultragraph shift spaces.

Findings

Established a Curtis-Hedlund-Lyndon type theorem for ultragraph shift spaces.

Provided a complete characterization of continuous, shift-commuting, length-preserving maps.

Connected the structure of these maps with generalized sliding block codes.

Abstract

Recently a generalization of shifts of finite type to the infinite alphabet case was proposed, in connection with the theory of ultragraph C*-algebras. In this work we characterize the class of continuous shift commuting maps between these spaces. In particular, we prove a Curtis-Hedlund-Lyndon type theorem and use it to completely characterize continuous, shift commuting, length preserving maps in terms of generalized sliding block codes.