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

  • MAHSA ALLAHBAKHSHI (a1), SOONJO HONG (a1) and UIJIN JUNG (a2)

Abstract

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.

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

  • MAHSA ALLAHBAKHSHI (a1), SOONJO HONG (a1) and UIJIN JUNG (a2)

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