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Limit Sets of Cellular Automata Associated to Probability Measures

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Abstract

We introduce the concept of limit set associated to a cellular automaton (CA) and a shift invariant probability measure. This is a subshift whose forbidden blocks are exactly those, whose probabilities tend to zero as time tends to infinity. We compare this probabilistic concept of limit set with the concepts of attractors, both in topological and measure-theoretic sense. We also compare this notion with that of topological limit set in different dynamical situations.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University in Prague, Malostranské nám. 25, CZ-11800, Praha 1, Czechia

    Petr Kůrka

  2. Departamento de Ingeniería Matemática, Universidad de Chile, casilla 170/3 correo 3, Santiago, Chile

    Alejandro Maass

Authors
  1. Petr Kůrka
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  2. Alejandro Maass
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Kůrka, P., Maass, A. Limit Sets of Cellular Automata Associated to Probability Measures. Journal of Statistical Physics 100, 1031–1047 (2000). https://doi.org/10.1023/A:1018706923831

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  • DOI: https://doi.org/10.1023/A:1018706923831

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