Measures of maximal relative entropy

Abstract

Given an irreducible subshift of finite type X, a subshift Y, a factor map π: X \to Y, and an ergodic invariant measure νon Y, there can exist more than one ergodic measure on X which projects to νand has maximal entropy among all measures in the fiber, but there is an explicit bound on the number of such maximal entropy preimages.

22 pages. (To appear in Erg. Th. Dyn. Sys.)