On a zero speed sensitive cellular automaton

Using an unusual yet natural invariant measure we show that there exists a sensitive cellular automaton whose perturbations propagate at an asymptotically null speed for almost all configurations. More specifically, we prove that Lyapunov exponents measuring pointwise or average linear speeds of the faster perturbations are equal to zero. We show that this implies the nullity of the measurable entropy. The measure μ we consider gives the μ-expansiveness property to the automaton. It is constructed with respect to a factor dynamical system based on simple ‘counter dynamics’. As a counterpart, we prove that in the case of positively expansive automata, the perturbations move at positive linear speed over all the configurations.

• Publication year

  2012

• Venue

  Nonlinearity

• Publication date

  2012-06-26

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1088/0951-7715/20/1/002arXiv 1206.5924
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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