2007/10/19 by Marcus Pivato, Pivato, Marcus, Reem Yassawi +1
Computer Science · Mathematics · Physics and Astronomy · #37B10 #37B15 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · doi:10.48550/arxiv.0710.3608
openalex publication_date 2007/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Many dynamical systems can be naturally represented as `Bratteli-Vershik' (or `adic') systems, which provide an appealing combinatorial description of their dynamics. If an adic system X satisfies two technical conditions (`focus' and `bounded width') then we show how to represent X using a two-dimensional subshift of finite type Y; each `row' in a Y-admissible configuration corresponds to an infinite path in the Bratteli diagram of X, and the vertical shift on Y corresponds to the `successor' map of X. Any Y-admissible configuration can then be recoded as the spacetime diagram of a one-dimensional cellular automaton F; in this way X is `embedded' in F (i.e. X is conjugate to a subsystem of F). With this technique, we can embed many odometers, Toeplitz systems, and constant-length substitution systems in one-dimensional cellular automata.