On Lyapunov Exponents for Cellular Automata

We give a review of quantities describing the speed of propagation of perturbations with respect to a cellular automaton (CA) and an invariant measure. We consider, as these quantities, the Lyapunov exponents of Shereshevsky [13], the average Lyapunov exponents of Tisseur [14] and the directional Lyapunov exponents defined and investigated by us in [6]. The directional Lyapunov exponents describe the propagation of a perturbation as observed in moving reference with a constant velocity to the right or to the left, as a function of the velocity. The directional entropy describes the randomness of the dynamics as observed in moving reference with constant velocity to the right or to the left as a function of the velocity. The main property discussed in the paper is the connection between all the above Lyapunov exponents and the entropies of a given CA.