On sofic-like shifts and flips

Abstract

We study generalizations of the notion of sofic shifts and the existence of flips for a shift space. Coded systems and almost sofic shifts generalize sofic shifts in terms of density of periodic points and entropies, respectively. An irreducible sofic shift is both coded and almost sofic. We investigate which properties of irreducible sofic shifts are extended to coded systems and almost sofic shifts.

We also study which shift-flip systems have infinitely many non-conjugate flips. We prove that if an infinite synchronized system has a flip, then there are countably many non-conjugate flips. However, this property can not be extended to coded systems. We construct a coded system which has only two non-conjugate flips.