Some Properties of topological pressure on cellular automata

Year 2014, , 41 - 51, 01.03.2014

Chih-Hung Chang

https://doi.org/10.13069/jacodesmath.66382

Cited By: 1

Abstract

This paper investigates the ergodicity and the power rule of the topological pressure of a cellular automaton. If a cellular automaton is either leftmost or rightmost premutive (due to the terminology given by Hedlund [Math.~Syst.~Theor.~3, 320-375, 1969]), then it is ergodic with respect to the uniform Bernoulli measure. More than that, the relation of topological pressure between the original cellular automaton and its power rule is expressed in a closed form. As an application, the topological pressure of a linear cellular automaton can be computed explicitly.

Keywords

Cellular automata, Permutive, Ergodicity, Topological pressure

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