On generalized compensation functions for factor maps between shift spaces on countable alphabets

Abstract

We show the existence of generalized compensation functions for a particular type of one-block factor maps [Formula: see text] between countable subshifts [Formula: see text] and [Formula: see text]. For factor maps between compact spaces, continuous compensation functions were studied by Walters in relation to the theory of relative pressure. Applying the thermodynamic formalism for sequences on countable subshifts, we generalize some existing results on factor maps between compact spaces to non-compact spaces. For related questions, we also study the existence of a preimage measure on [Formula: see text] of an invariant measure on [Formula: see text], and their relations.