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Abstract
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We show that, for every positive real number
and every positive
integer
, there exist
oriented graphs
(with countably many vertices) that are strongly connected, of period
, of Gurevich
entropy
, and
such that
is positive recurrent (thus the topological Markov chain on
admits a measure of
maximal entropy) and
is transient (thus the topological Markov chain on
admits no measure of maximal entropy).
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Keywords
topological Markov chain, countable oriented graph,
topological entropy
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Mathematical Subject Classification 2010
Primary: 37B10
Secondary: 37B40
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Milestones
Received: 26 June 2018
Accepted: 8 July 2019
Published: 21 December 2019
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