HAL: hal-00089100, version 3

arXiv: math/0608240

DOI: 10.1016/j.aam.2008.08.001

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Advances in Applied Mathematics 42, 4 (2009) 504-518

Available versions:

v1 (2006-08-10)

v2 (2012-06-29)

v3 (2012-06-30)

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

Pierre Tisseur 1

(2009-05-04)

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).

1:	Centro de Matematica, Computação e Cognição (CMCC)
	UFABC

Subject

:

Mathematics/Dynamical Systems

Keyword(s): Cellular Automata – discrete dynamical systems

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From: Pierre Tisseur <>

Submitted on: Friday, 29 June 2012 21:42:10

Updated on: Saturday, 30 June 2012 12:24:33