Embedding Bratteli-Vershik systems in cellular automata
| dc.creator | Pivato, Marcus | |
| dc.creator | Yassawi, Reem | |
| dc.date | 2007-10-19 | |
| dc.date.accessioned | 2026-07-07T08:37:17Z | |
| dc.date.available | 2026-07-07T08:37:17Z | |
| dc.description | 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. | |
| dc.description | 12 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/0710.3608 | |
| dc.identifier | http://arxiv.org/abs/0710.3608 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140349 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37B15, 37B10 | |
| dc.title | Embedding Bratteli-Vershik systems in cellular automata | |
| dc.type | text |