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arXiv · 1201.1622

Orbit equivalent substitution dynamical systems and complexity

S. Bezuglyi·O. Karpel
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Abstract

For any primitive proper substitution σ, we give explicit constructions of countably many pairwise non-isomorphic substitution dynamical systems {(X_{ζ_n}, T_{ζ_n})}_{n=1}^{\infty} such that they all are (strong) orbit equivalent to (X_σ, T_σ). We show that the complexity of the substitution dynamical systems {(X_{ζ_n}, T_{ζ_n})} is essentially different that prevents them from being isomorphic. Given a primitive (not necessarily proper) substitution τ, 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_τ, T_τ).

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S. Bezuglyi, O. Karpel. 2012-01-08. Orbit equivalent substitution dynamical systems and complexity. https://arxiv.org/abs/1201.1622

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