An application of the ergodic theorem of information theory to Lyapunov exponents of cellular automata (Q388660)

In this work a sound proof is given of the relation between entropy and Lyapunov exponents of cellular automata. It parallels the Ruelle and Pesin inequalities for smooth dynamical systems, and was first put forward by \textit{M. A. Shereshevsky} [J. Nonlinear Sci. 2, No. 1, 1--8 (1992; Zbl 0872.58038)], but the latter author's proof apparently contains errors and was somewhat too brief. The authors of this paper provide a new proof of the so-called Shereshevsky inequality.NEWLINENEWLINEThe topic addressed by this paper is very important as it constitutes a further step towards a complete understanding of the dynamics of cellular automata from a quantitative point of view.