## On the Vere-Jones classification and existence of maximal measure
for topological Markov chains

*Pacific J. Math.*, **209**, No. 2, 365-380, 2003.

### Abstract

We consider topological Markov chains (also called Markov shifts) on
countable graphs.
We show that a transient graph can be extended to a recurrent graph of
equal entropy which is either positive recurrent of null recurrent, and we
give an example of each type.
We extend the notion of *local entropy* to topological
Markov chains and prove that a
transitive Markov chain admits a measure of maximal entropy (or *maximal
measure*) whenever its local entropy is less than its (global) entropy.

Paper:
[arXiv:1901.00339]
[pdf (published paper)]
[Paper on Pacific J.
Math. website (free)]