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Pivato, Marcus and Yassawi, Reem
(2010).
DOI: https://doi.org/10.1017/S0143385709000601
Abstract
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 is linearly recurrent, 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 space-time diagram of a one-dimensional cellular automaton Φ; in this way X is embedded in Φ (i.e. X is conjugate to a subsystem of Φ). With this technique, we can embed many odometers, Toeplitz systems, and constant-length substitution systems in one-dimensional cellular automata.
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About
- Item ORO ID
- 67099
- Item Type
- Journal Item
- ISSN
- 0143-3857
- Project Funding Details
-
Funded Project Name Project ID Funding Body Not Set Not Set NERSC - Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Copyright Holders
- © 2009 Cambridge University Press
- Depositing User
- Reem Yassawi