An invariant for bounded-to-one factor maps between transitive sofic subshifts

Abstract

AbstractWe define a ‘core-matrix’ of a transitive sofic subshift, which is unique up to similarity for each transitive sofic subshift. We prove that if there exists a bounded-to-one factor map from one transitive sofic subshift to another, the block of the Jordan form of a core-matrix of this second subshift with non-zero eigenvalues is a principal submatrix of the Jordan form of a core-matrix of the first. We also prove that the subshifts that are almost of finite type are ‘spectrally of finite type’.