Space-time directional Lyapunov exponents for cellular automata (Q858038)

Lyapunov exponents for cellular automata were first introduced by \textit{S. Wolfram} [Cellular automata and complexity. Collected papers. Reading, MA: Addison-Wesley Publishing Company (1994; Zbl 0823.68003)] to characterize the instability of their dynamics, in analogy to that shown by differentiable dynamical systems under perturbations of initial conditions. A rigorous mathematical definition of these exponents for one-dimensional automata was given by \textit{M. A. Shereshevsky} [J. Nonlinear Sci. 2, No.~1, 1--8 (1992; Zbl 0872.58038)] in the framework of ergodic theory. The present authors attempt to account for the space-time complexity of the automata, by generalizing the Shereshevsky exponents to space-time directional Lyapunov exponents, and next relating them to the directional entropy.