Abstract

We show the existence of generalized compensation functions for a particular type of one-block factor maps π:X → Y between countable subshifts X and Y. 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 X of an invariant measure on Y, and their relations.