Encyclopedia of Complexity and Systems Science

2009 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Dynamics of Cellular Automata in Non-compact Spaces

  • Enrico Formenti
  • Petr Kůrka
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30440-3_138

Definition of the Subject

In topological dynamics, the assumption of compactness is usually adopted as it has farreaching consequences. Each compact dynamical system has an almost periodic point, containsa minimal subsystem, and each trajectory has a limit point. Nevertheless, there areimportant examples of non‐compact dynamical systems like linear systems on\( { \mathbb{R}^n }\)

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We thank Marcus Pivato and Francois Blanchard for careful reading of the paper and many valuable suggestions. The research waspartially supported by the Research Program Project “Sycomore” (ANR-05-BLAN-0374).


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Enrico Formenti
    • 1
  • Petr Kůrka
    • 2
  1. 1.Laboratoire I3S – UNSA/CNRS UMR 6070Université de Nice Sophia AntipolisSophia AntipolisFrance
  2. 2.Center for Theoretical StudyAcademy of Sciencesand Charles UniversityPragueCzech Republic