On a zero speed sensitive cellular automaton

Xavier Bressaud (1) , Pierre Tisseur (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 CMCC - Centro de Matematica, Computação e Cognição

Using an unusual, yet natural invariant measure we show that there exists a sensitive cellular automaton whose perturbations propagate at 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 m we consider gives the m-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.

Mots clés: 37B15; 37A35; 37A25; 37A60; 37A05

Domaines: Systèmes dynamiques [math.DS]

Xavier Bressaud, Pierre Tisseur. On a zero speed sensitive cellular automaton. Nonlinearity, 2006, 20, pp.1-19. ⟨10.1088/0951-7715/20/1/002⟩. ⟨hal-00711869⟩