# American Institute of Mathematical Sciences

February  2019, 39(2): 1033-1048. doi: 10.3934/dcds.2019043

## Continuous shift commuting maps between ultragraph shift spaces

 UFSC – Department of Mathematics, 88040-900 Florianópolis - SC, Brazil

* Corresponding author: marcelo.sobottka@ufsc.br

Received  March 2018 Revised  August 2018 Published  November 2018

Fund Project: D. Gonçalves was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPq. M. Sobottka was supported by CNPq-Brazil PQ grant

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.

Citation: Daniel Gonçalves, Marcelo Sobottka. Continuous shift commuting maps between ultragraph shift spaces. Discrete & Continuous Dynamical Systems - A, 2019, 39 (2) : 1033-1048. doi: 10.3934/dcds.2019043
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