#### Vol. 303, No. 1, 2019

 Recent Issues Vol. 307: 1  2 Vol. 306: 1  2 Vol. 305: 1  2 Vol. 304: 1  2 Vol. 303: 1  2 Vol. 302: 1  2 Vol. 301: 1  2 Vol. 300: 1  2 Online Archive Volume: Issue:
 The Journal Subscriptions Editorial Board Officers Contacts Submission Guidelines Submission Form Policies for Authors ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Special Issues Author Index To Appear Other MSP Journals
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 $G,{G}^{\prime }$ (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 ${G}^{\prime }$ is transient (thus the topological Markov chain on ${G}^{\prime }$ admits no measure of maximal entropy).

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/pjm

We have not been able to recognize your IP address 18.215.33.158 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

##### Keywords
topological Markov chain, countable oriented graph, topological entropy
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