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ORBIT EQUIVALENT SUBSTITUTION DYNAMICAL SYSTEMS AND COMPLEXITY
Journal article   Open access   Peer reviewed

ORBIT EQUIVALENT SUBSTITUTION DYNAMICAL SYSTEMS AND COMPLEXITY

S Bezuglyi and O Karpel
Proceedings of the American Mathematical Society, Vol.142(12), pp.4155-4169
01/01/2014
DOI: 10.1090/S0002-9939-2014-12139-3
url
https://doi.org/10.1090/S0002-9939-2014-12139-3View
Published (Version of record) Open Access

Abstract

For any primitive proper substitution sigma, we give explicit constructions of countably many pairwise non-isomorphic substitution dynamical systems {(X-zeta n, T-zeta n)}(n=1)(infinity) such that they all are (strong) orbit equivalent to (X-sigma, T-sigma). We show that the complexity of the substitution dynamical systems {(X-zeta n, T-zeta n)} is the essential difference that prevents them from being isomorphic. Given a primitive (not necessarily proper) substitution tau, we find a stationary simple properly ordered Bratteli diagram with the least possible number of vertices such that the corresponding Bratteli-Vershik system is orbit equivalent to (X-tau, T-tau).
Mathematics Physical Sciences Mathematics, Applied Science & Technology

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