Continuous shift commuting maps between ultragraph shift spaces

Daniel Gonçalves; Marcelo Sobottka

doi:10.3934/dcds.2019043

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2019, Volume 39, Issue 2: 1033-1048. Doi: 10.3934/dcds.2019043

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Continuous shift commuting maps between ultragraph shift spaces

Daniel Gonçalves and
Marcelo Sobottka^,

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

* Corresponding author: marcelo.sobottka@ufsc.br
* Corresponding author: marcelo.sobottka@ufsc.br

Received: March 1, 2018

Revised: August 1, 2018

Published online: February 1, 2019

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

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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.

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Mathematics Subject Classification: Primary: 37B10, 54H20; Secondary: 37B15.

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