Construction of µ-limit Sets

Laurent Boyer (1) , Martin Delacourt (2) , Mathieu Sablik (3)

1 LAMA - Laboratoire de Mathématiques
2 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166
3 LATP - Laboratoire d'Analyse, Topologie, Probabilités

The µ-limit set of a cellular automaton is a subshift whose forbidden patterns are exactly those, whose probabilities tend to zero as time tends to infinity. In this article, for a given subshift in a large class of subshifts, we propose the construction of a cellular automaton which realizes this subshift as µ-limit set where µ is the uniform Bernoulli measure.

Keywords: cellular automata; recursively enuerable subshift; limit set; measure-theoretic dynamical system

Domains: Other [cs.OH]

Laurent Boyer, Martin Delacourt, Mathieu Sablik. Construction of µ-limit Sets. Journées Automates Cellulaires 2010, Dec 2010, Turku, Finland. pp.76-87. ⟨hal-00542356⟩