Structure of transition classes for factor codes on shifts of finite type
Mahsa Allahbakhshi, Soonjo Hong, Uijin Jung · Ergodic Theory and Dynamical Systems · 2014
Given a factor code ${\it\pi}$ from a shift of finite type $X$ onto a sofic shift $Y$ , the class degree of ${\it\pi}$ 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.