An application of the ergodic theorem of information theory to Lyapunov exponents of cellular automata - Bułatek, Wojciech; Courbage, Maurice; Kamiński, Brunon; Szymański, Jerzy (Topological Methods in Nonlinear Analysis, 2012)
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.