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Strong shift equivalence of 2 by 2 non-negative integral matrices

Part of:Measure-theoretic ergodic theory

Published online by Cambridge University Press:  26 February 2010

Geon Ho Choe and
Sujin Shin
Geon Ho Choe
Affiliation:
Department of Mathematics, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea, e-maii: choet@euclid.kaist.ac.kr
Sujin Shin
Affiliation:
Department of Mathematics, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea
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Abstract

It is known that if A and B are nontriangular 2 × 2 non-negative integral matrices similar over the integers and –tr A ≤det A, then A and B are strongly shift equivalent. Suppose that A and B are 2 × 2 non-negative integral matrices similar over the integers. In this article it is shown that if –2 tr A≤det A <– tr A and if | det A | is not a prime, then A and B are strongly shift equivalent.

MSC classification

Secondary:28D05: Measure-preserving transformations

Information

Type
Research Article
Information
Mathematika , Volume 44 , Issue 2 , December 1997, pp. 302 - 312
Copyright
Copyright © University College London 1997

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References

1.Baker, K. A.. Strong shift equivalence and shear adjacency of nonnegative square integer matrices. Linear Algebra Appl., 93 (1987), 131147.CrossRefGoogle Scholar
2.Baker, K. A.. Strong shift equivalence of 2 by 2 matrices of nonnegative integers. Erg. Theory Dyn. Syst., 3 (1983), 501–508.Google Scholar
3.Boyle, M.. Shift equivalence and the Jordan form away from zero. Erg. Theory Dyn. Syst., 4 (1984). 367–380.Google Scholar
4.Boyle, M.. The stochastic shift equivalence conjecture is false. Conlemp. Math., 135 (1992), 107–110.Google Scholar
5.Cuntz, J. and Krieger, W.. Topological Markov chains with dicyclic dimension groups. J. Reine Angew. Math., 320 (1980), 4451.Google Scholar
6.Kim, K. H. and Roush, F. W.. Williams's conjecture is false for reducible subshifts. J. Amer. Math. Soc., 5 (1992), 213–215.Google Scholar
7.Lind, D. and Marcus, B.. An Introduction to Symbolic Dynamics and Coding (Cambridge Univ. Press, New York, 1995).CrossRefGoogle Scholar
8.Parry, W. and Williams, R. F.. Block coding and a zeta function for finite Markov chains. Proc. London Math. Soc., 25 (1977), 483495.CrossRefGoogle Scholar
9.Wagoner, J. B.. Classification of subshifts of finite type revisited. Contemp. Math., 135 (1992), 423–444.CrossRefGoogle Scholar
10.Williams, R. F.. Classification of subshifts of finite type. Ann. of Math., 98 (1973), 120–153; Errata Ann. of Math., 99 (1974), 380 381.Google Scholar
11.Williams, R. F.. Strong shift equivalence of matrices in GL(2, ℤ). Contemp. Math., 135 (1992), 445–451.Google Scholar