Ergodic Theory and Dynamical Systems

Research Article

Strong shift equivalence of 2 × 2 matrices of non-negative integers

Kirby A. Bakera1

a1 Department of Mathematics, UCLA, California, CA 90024, USA


The concept of strong shift equivalence of square non-negative integral matrices has been used by R. F. Williams to characterize topological isomorphism of the associated topological Markov chains. However, not much has been known about sufficient conditions for strong shift equivalence even for 2×2 matrices (other than those of unit determinant). The main theorem of this paper is: If A and B are positive 2×2 integral matrices of non-negative determinant and are similar over the integers, then A and B are strongly shift equivalent.

(Received January 20 1982)

(Revised September 15 1983)