Vol. 303, No. 1, 2019

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

Sylvie Ruette

Vol. 303 (2019), No. 1, 317–323
DOI: 10.2140/pjm.2019.303.317
Abstract

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).

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