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Article Dans Une Revue Advances in Applied Mathematics Année : 2009

Density of periodic points, invariant measures and almost equicontinuous points of cellular automata

Résumé

Revisiting the notion of m-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure m by iterations of a m-almost equicontinuous automata F, converges in Cesaro mean to an invariant measure mc. If the initial measure m is a Bernouilli measure, we prove that the Cesaro mean limit measure mc is shift mixing. Therefore we also show that for any shift ergodic and F-invariant measure m, the existence of m-almost equicontinuous points implies that the set of periodic points is dense in the topological support S(m) of the invariant measure m. Finally we give a non trivial example of a couple (m-equicontinuous cellular automata F, shift ergodic and F-invariant measure m) which has no equicontinuous point in S(m).
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Dates et versions

hal-00089100 , version 1 (10-08-2006)
hal-00089100 , version 2 (28-06-2012)
hal-00089100 , version 3 (29-06-2012)

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Citer

Pierre Tisseur. Density of periodic points, invariant measures and almost equicontinuous points of cellular automata. Advances in Applied Mathematics, 2009, 42 (4), pp.504-518. ⟨10.1016/j.aam.2008.08.001⟩. ⟨hal-00089100v3⟩

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