### An application of the ergodic theorem of information theory to Lyapunov exponents of cellular automata

DOI: http://dx.doi.org/10.12775/TMNA.2012.039

#### Abstract

We prove a generalization of the individual ergodic theorem of the information theory and we apply it to give a new proof of the Shereshevsky inequality connecting the metric entropy and Lyapunov exponents of dynamical systems generated by cellular automata.

#### Keywords

Cellular automata; dynamical systems; entropy; local entropy; Lyapunov exponents

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