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In this chapter we investigate the problem of determining when two subshifts of finite type are the “same”. Two subshifts of finite type are dynamically the same if there is a homeomorphism between them which commutes with the shifts. We examine this problem for both one and two-sided subshifts of finite type. In the one-sided setting we develop a simple algorithm which allows us to determine when two one-sided subshifts of finite type are the same. In the two-sided setting we will see that it is not known whether such an algorithm can exist.
KeywordsTransition Matrix Finite Type Transition Matrice Inverse Limit Dimension Group
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- [HR]E. Hewitt and K. Ross, Abstract Harmonic Analysis, Academic Press and Springer-Verlag, 1963.Google Scholar
- [KR1]K.H. Kim and F. Roush, Decidability of Shift Equivalence, Dynamical Systems: Proceedings, University of Maryland 1886–87 (J.C. Alexander, ed.), Springer-Verlag, 1988, pp. 374–424.Google Scholar
- [PT]W. Parry and S. Tuncel, Classification Problems in Ergodic Theory London Mathematical Society Lecture Series, 67, Cambridge University Press, 1982.Google Scholar
- [Wi1]R.F. Williams, Classification of One-dimensional Attractors, in Global Analysis, Proceedings of Symposia in Pure and Applied Math (S-S. Chern and S. Smale, eds.), vol. XIV, American Mathematical Society, 1970, pp. 341–361.Google Scholar