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

### 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).

Paper:
[arXiv:1806.00214]
[pdf]