Relative entropy functions for factor maps between subshifts

Abstract

Let ( X, S) and ( Y, T) be topological dynamical systems and pi : X -> Y a factor map. A function F epsilon C( X) is a compensation function for pi if P( F + phi o p) = P(phi) for all phi epsilon C( Y). For a factor code between subshifts of finite type, we analyze the associated relative entropy function and give a necessary condition for the existence of saturated compensation functions. Necessary and sufficient conditions for a map to be a saturated compensation function will be provided.