Some Ergodic Properties of One-Dimensional Invertible Cellular Automata
Chih-Hung Chang And Hasan Akin
In this paper we consider invertible one-dimensional linear cellular automata (CA hereafter) defined on a finite alphabet of cardinality m ∈ N, m ≥ 2. Under some assumptions we prove that every invertible one-dimensional linear CA and its inverse are strong mixing. We also prove that every invertible one-dimensional linear CA is a Bernoulli automorphism without making use of the natural extension previously used in the literature.
Keywords: Measure-preserving transformation, invertible cellular automata, strong mixing, bernoulli automorphism
1991 Mathematics Subject Classification: Primary 37A05; Secondary 37B15, 28D20