Orbit equivalent substitution dynamical systems and complexity

2012/01/08 by Sergey Bezuglyi, Bezuglyi, S., Olena Karpel +1
Biochemistry, Genetics and Molecular Biology · Computer Science · #37B05 (Secondary) #37B10 (Primary) 37A20 #Chemical Synthesis and Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #Fractal and DNA sequence analysis #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1201.1622

openalex publication_date 2012/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any primitive proper substitution σ, we give explicit constructions of countably many pairwise non-isomorphic substitution dynamical systems (X_ζn, T_ζn)_n=1^∞ such that they all are (strong) orbit equivalent to (X_σ, T_σ). We show that the complexity of the substitution dynamical systems (X_ζn, T_ζn) 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).

Related

• Aperiodic substitutional systems and their Bratteli diagrams
• The K-group of substitutional systems
• Necessary and sufficient conditions for a dynamical system to be\n topologically conjugate to a given substitution minimal system
• Transformations, Dynamics and Complexity
• On orbit complexity of dynamical systems: intermediate value property and level set related to a Furstenberg problem