Institut
de Mathématiques de Luminy

Abstract 2001-21 |

**Ruette** Sylvie.

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

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. |