The Walters condition

We discuss a regularity condition introduced by Walters in 1978 for the nee ds of the thermodynamic formalism. We show that it is the "right" regularit y condition to require in a large class of problems, including the thermody namic formalism as well as the study of maximising measures. and the search of normal forms modulo coboundaries of continuous functions. (C) 2001 Edit ions scientifiques et medicales Elsevier SAS.