About a low complexity class of Cellular Automata
Dynamical Systems
2012-06-28 v2
Abstract
Extending to all probability measures the notion of m-equicontinuous cellular automata introduced for Bernoulli measures by Gilman, we show that the entropy is null if m is an invariant measure and that the sequence of image measures of a shift ergodic measure by iterations of such automata converges in Cesaro mean to an invariant measure mc. Moreover this cellular automaton is still mc-equicontinuous and the set of periodic points is dense in the topological support of the measure mc. The last property is also true when m is invariant and shift ergodic.
Cite
@article{arxiv.1206.5925,
title = {About a low complexity class of Cellular Automata},
author = {Pierre Tisseur},
journal= {arXiv preprint arXiv:1206.5925},
year = {2012}
}