On the number of fixed points of sofic flip systems

Abstract

In the case when $X$ is a sofic shift and $ϕ: X \to X$ is a homeomorphism such that $ϕ^2 = \text{id}_X$ and $ϕσ_X = σ_X^{-1} ϕ$, the number of points in $X$ that are fixed by $σ_X^m$ and $σ_X^n ϕ$, $m=1,2,...$, $n\in\Bbb Z$, is expressed in terms of a finite number of square matrices: The matrices are obtained from Krieger's joint state chain of a sofic shift which is conjugate to $X$.