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| HAL : hal-00089100, version 3 |
| arXiv : math/0608240 |
| DOI : 10.1016/j.aam.2008.08.001 |
| Fiche détaillée |  Récupérer au format |
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| Advances in Applied Mathematics 42, 4 (2009) 504-518 |
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| Versions disponibles : | v1 (10-08-2006) | v2 (29-06-2012) | v3 (30-06-2012) |
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| Density of periodic points, invariant measures and almost equicontinuous points of cellular automata |
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| Pierre Tisseur 1 |
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| (04/05/2009) |
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| 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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| 1 : | Centro de Matematica, Computação e Cognição (CMCC) |
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UFABC |
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| Domaine | : | Mathématiques/Systèmes dynamiques |
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| Cellular Automata – discrete dynamical systems |
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| hal-00089100, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00089100 | |
| oai:hal.archives-ouvertes.fr:hal-00089100 | |
| Contributeur : Pierre Tisseur | |
| Soumis le : Vendredi 29 Juin 2012, 21:42:10 | |
| Dernière modification le : Samedi 30 Juin 2012, 12:24:33 | |
