Cellular automata in the Cantor, Besicovitch and Weyl spaces

Abstract : The Besicovitch and Weyl pseudometrics on the space $A^{\ZZ}$ of biinfinite sequences measure the density of differences in either the central or arbitrary segments of given sequences. The Besicovitch and Weyl spaces are obtained from $A^{\ZZ}$ by factoring through the equivalence of zero distance. We consider cellular automata as dynamical systems on the Besicovitch and Weyl spaces and compare their topological and dynamical properties with those in the Cantor space.
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Francois Blanchard, Enrico Formenti, Petr Kurka. Cellular automata in the Cantor, Besicovitch and Weyl spaces. [Research Report] LIP RR-1998-31, Laboratoire de l'informatique du parallélisme. 1998, 2+14p. ⟨hal-02101951⟩

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