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Abstract: We investigate topological and ergodic properties of cellular automata having equicontinuity points. In this class surjectivity on a transitive SFT implies existence of a dense set of periodic points. Our main result is that under the action of such an automaton any shift--ergodic measure converges in Cesaro mean, assuming equicontinuity points have measure 1; the limit measure is described by a formula and some of the properties of its topological support are given. (Update)
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.... of periodic points Comment The answer is positive for additive CA, see [11] and also for surjective equicontinuous cellular automata [7]. 2.2.3 Besicovitch and Weyl topologies Open Problem 9 : Transitivity Are there transitive cellular automata for Besicovitch or Weyl...
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BibTeX entry: (Update)
F. Blanchard and P. Tisseur, S'ome properties of cellular automata with equiconti- nuity points, Annales de l'Institut Henri Poincar, 2000, to appear. http://citeseer.ist.psu.edu/blanchard00some.html More
@misc{ blanchard00isseur,
author = "F. Blanchard",
title = "isseur, S'ome properties of cellular automata with equiconti- nuity points",
text = "F. Blanchard and P. Tisseur, S'ome properties of cellular automata with
equiconti- nuity points, Annales de l'Institut Henri Poincar, 2000, to appear.",
year = "2000",
url = "citeseer.ist.psu.edu/blanchard00some.html" }
Citations (may not include all citations):114 Theory and applications of cellular automata (context) - Wolfram - 1986
53 Ergodic theory on compact spaces (context) - Denker, Grillenberger et al. - 1975
46 Endomorphisms and automorphisms of the shift dynamical syste.. (context) - Hedlund - 1969
13 Applications of ergodic theory and sofic systems to cellular.. (context) - Lind - 1984
7 Classes of linear automata (context) - Gilman - 1987
4 the entropy geometry of cellular automata (context) - Milnor - 1988
3 Entropies of automorphisms of a topological Markov shift (context) - Lind - 1987
2 Endomorphisms of irreducible shifts of finite type (context) - Coven, Paul - 1974
1 Periodic points in cellular automata (context) - Boyle, Kitchens - 1999
1 Dynamical behaviour of Coven's aperiodic cellular automata (context) - Blanchard, Maass - 1996
1 On sofic limit sets of cellular automata (context) - Maass - 1995
1 equicontinuity and attractors in linear cellular automata (context) - urka - 1997
1 On Cesaro limit distribution of a classof permutative cellul.. (context) - Maass, nez - 1998
1 Cesaro mean distribution of group automata starting from mea.. (context) - Ferrari, Maass et al. - 1999
Documents on the same site (http://pierre.tisseur.free.fr/):
A Bilateral Version of the Shannon-McMillan-Breiman Theorem - Tisseur (2003) (Correct)
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