Communications in Mathematical Physics

, Volume 136, Issue 3, pp 599–605 | Cite as

On ergodic one-dimensional cellular automata

  • M. Shirvani
  • T. D. Rogers


We show that all onto cellular automata defined on the binary sequence space are invariant with respect to the Haar measure, and that an extensive class of such maps (including many nonlinear ones) are strongly mixing with respect to the Haar measure.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Cellular Automaton 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • M. Shirvani
    • 1
  • T. D. Rogers
    • 1
  1. 1.Department of MathematicsUniversity of AlbertaEdmontonCanada

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