Bounded-to-1 factors of an aperiodic shift of finite type are 1-to-1 almost everywhere factors also
Jonathan J. Ashley · Ergodic Theory and Dynamical Systems · 1990
Abstract We show that if π: ΣG → ΣH is a bounded-to-1 factor map from an irreducible shift of finite type ΣG with period pG to a shift of finite type ΣH with period pH, then there is a factor map that is (pG/pH)-to-1 almost everywhere. Moreover, if π is right closing, then may be taken to be right closing also.