Bounded-to-1 factors of an aperiodic shift of finite type are 1-to-1 almost everywhere factors also

Abstract

Abstract We show that if π: Σ G → Σ H is a bounded-to-1 factor map from an irreducible shift of finite type Σ G with period p G to a shift of finite type Σ H with period p H , then there is a factor map that is ( p G / p H )-to-1 almost everywhere. Moreover, if π is right closing, then may be taken to be right closing also.