Strong shift equivalence of 2 × 2 matrices of non-negative integers
- 19 September 1983
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 3 (4) , 501-508
- https://doi.org/10.1017/s0143385700002091
Abstract
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.Keywords
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