The Lind Zeta Function and Williams' Decomposition Theorem for Sofic Shift-Reversal Systems of Finite Order

Abstract

We establish the Lind zeta function for automorphisms of shift spaces of finite order and introduce the generating function of shift-flip systems. A decomposition theorem for the Lind zeta function for reversal systems of finite order is established: we express it in terms of the Lind zeta function for automorphism and the generating functions of flip systems. In the sofic case, the Lind zeta function for reversal systems of finite order can be expressed in terms of matrices.

An analogue of Williams' decomposition theorem for reversal systems of finite order is established. To this end, we introduce the concept of half elementary conjugacy. Every conjugacy between two sofic shift-reversal systems of finite order can be decomposed into the composition of an even number of such half elementary conjugacies.