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arXiv · 1410.7425

Limit behaviour of $μ-$equicontinuous cellular automata

Felipe García-Ramos
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Abstract

The concept of $μ-$equicontinuity was introduced by Gilman to classify cellular automata. We show that under some conditions the sequence of Cesaro averages of a measure $μ,$ converge under the actions of a $μ-$equicontinuous CA. We address questions raised by Blanchard-Tisseur on whether the limit measure is either shift-ergodic, a uniform Bernoulli measure or ergodic with respect to the CA. Many of our results hold for CA on multidimensional subshifts.

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Felipe García-Ramos. 2015-09-15. Limit behaviour of $μ-$equicontinuous cellular automata. https://doi.org/10.1016/tcs2015.08.010

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