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arXiv · 1806.00214

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

Sylvie Ruette
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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, 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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Sylvie Ruette. 2018-06-01. Topological Markov chains of given entropy and period with or without measure of maximal entropy. https://doi.org/10.2140/pjm.2019.303.317

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