Structure of transition classes for factor codes on shifts of finite type

Abstract

Given a factor code pi from a shift of finite type X onto a sofic shift Y, the class degree of pi is defined to be the minimal number of transition classes over the points of Y. In this paper, we investigate the structure of transition classes and present several dynamical properties analogous to the properties of fibers of finite-to-one factor codes. As a corollary, we show that for an irreducible factor triple, there cannot be a transition between two distinct transition classes over a right transitive point, answering a question raised by Quas.