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Chaotic Subshifts Generated by One Dimensional Elementary CA. The Role of Transitivity

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Cellular Automata (ACRI 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2493))

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Abstract

We present the behavior of simple subshifts generated by 1D Elementary CA (ECA) with respect to some components of chaoticity as transitivity, topological mixing and strong transitivity. A classification of subshifts generated by ECA with respect to transitivity is given. In literature one can find several notions of topological transitivity. We discuss two types of transitivity for discrete time dynamical system: positive and full. The relationships among these notions and properties such as existence of a dense orbit, topological chaos and indecomposability are investigated.

This work has been supported by M.I.U.R. COFIN project ”Formal Languages and Automata: Theory and Application”

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Via Bicocca degli Arcimboldi 8, 20126, Milano, Italy

    Gianpiero Cattaneo & Alberto Dennunzio

Authors
  1. Gianpiero Cattaneo
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  2. Alberto Dennunzio
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Editors and Affiliations

  1. Department of Computer Science, Systems and Communication, University of Milano-Bicocca, Via Bicocca degli Arcimboldi, 8, 20126, Milan, Italy

    Stefania Bandini

  2. Computer Science Department, University of Geneva, 24, Rue du General Dufour, 1211, Geneva 4, Switzerland

    Bastien Chopard

  3. Computer Science Institute Faculty of Sciences, University of Lausanne, 1015, Lausanne, Switzerland

    Marco Tomassini

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© 2002 Springer-Verlag Berlin Heidelberg

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Cattaneo, G., Dennunzio, A. (2002). Chaotic Subshifts Generated by One Dimensional Elementary CA. The Role of Transitivity. In: Bandini, S., Chopard, B., Tomassini, M. (eds) Cellular Automata. ACRI 2002. Lecture Notes in Computer Science, vol 2493. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45830-1_8

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  • DOI: https://doi.org/10.1007/3-540-45830-1_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44304-9

  • Online ISBN: 978-3-540-45830-2

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