Ergodic Theory and Dynamical Systems

Given a factor code π from a shift of finite type X onto a sofic shift Y , the class degree of π 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.