Journal article
ORBIT EQUIVALENT SUBSTITUTION DYNAMICAL SYSTEMS AND COMPLEXITY
Proceedings of the American Mathematical Society, Vol.142(12), pp.4155-4169
01/01/2014
DOI: 10.1090/S0002-9939-2014-12139-3
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).
Details
- Title: Subtitle
- ORBIT EQUIVALENT SUBSTITUTION DYNAMICAL SYSTEMS AND COMPLEXITY
- Creators
- S Bezuglyi - Institute for Low Temperature Physics, Kharkov, UkraineO Karpel - Institute for Low Temperature Physics, Kharkov, Ukraine
- Resource Type
- Journal article
- Publication Details
- Proceedings of the American Mathematical Society, Vol.142(12), pp.4155-4169
- DOI
- 10.1090/S0002-9939-2014-12139-3
- ISSN
- 0002-9939
- eISSN
- 1088-6826
- Publisher
- American Mathematical Society
- Number of pages
- 15
- Language
- English
- Date published
- 01/01/2014
- Academic Unit
- Mathematics
- Record Identifier
- 9984241155802771
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