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

Published online by Cambridge University Press:  19 September 2008

Kirby A. Baker
Kirby A. Baker
Affiliation:
Department of Mathematics, UCLA, California, CA 90024, USA
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Abstract

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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 3 , Issue 4 , December 1983 , pp. 501 - 508
Copyright
Copyright © Cambridge University Press 1983

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