Transitive topological Markov chains of given entropy and period with or without measure of maximal entropy

We show that, for every positive real number $h$ and every positive integer $p$ , there exist oriented graphs $G, G^{'}$ (with countably many vertices) that are strongly connected, of period $p$ , of Gurevich entropy $h$ , and such that $G$ is positive recurrent (thus the topological Markov chain on $G$ admits a measure of maximal entropy) and $G^{'}$ is transient (thus the topological Markov chain on $G^{'}$ admits no measure of maximal entropy).

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Keywords

topological Markov chain, countable oriented graph, topological entropy

Mathematical Subject Classification 2010

Primary: 37B10

Secondary: 37B40

Milestones

Received: 26 June 2018

Accepted: 8 July 2019

Published: 21 December 2019

Authors

Sylvie Ruette
Laboratoire de Mathématiques d’Orsay, UMR 8628 Université Paris-Saclay Orsay France

Vol. 303, No. 1, 2019

Sylvie Ruette

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors