Limit behaviour of μ-equicontinuous cellular automata

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• 作者：Felipe Garcí ; a-Ramos ^{felipegra@math.ubc.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Cellular automata ; Topological dynamical systems ; Measurable dynamics ; Multidimensional subshifts ; Measure of maximal entropy
• 刊名：Theoretical Computer Science
• 出版年：2016
• 出版时间：11 April 2016
• 年：2016
• 卷：623
• 期：Complete
• 页码：2-14
• 全文大小：384 K

文摘

The concept of μ-equicontinuity was introduced in [12] 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 in [3] 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.