On the Vere-Jones classification and existence of maximal measure
for topological Markov chains
Pacific J. Math., 209, No. 2, 365-380, 2003.
We consider topological Markov chains (also called Markov shifts) on
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.
[pdf (published paper)]
[Paper on Pacific J.
Math. website (free)]