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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Mixing properties of one-dimensional
cellular automata


Author: Rune Kleveland
Journal: Proc. Amer. Math. Soc. 125 (1997), 1755-1766
MSC (1991): Primary 47A35, 22D25; Secondary 28D05, 46L05
MathSciNet review: 1363428
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Abstract: We study a class of endomorphisms on the space of bi-infinite sequences over a finite set, and show that such a map is onto if and only if it is measure-preserving. A class of dynamical systems arising from these endomorphisms are strongly mixing, and some of them even $m$-mixing. Some of these are isomorphic to the one-sided shift on $\mathbb {Z}_n$ in both the topological and measure-theoretical sense. Such dynamical systems can be associated to $\mathcal {O}_n$, the Cuntz-algebra of order $n$, in a natural way.


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Additional Information

Rune Kleveland
Affiliation: Department of Mathematics, University of Oslo, Box 1053, 0316 Oslo, Norway
Email: runekl@math.uio.no

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03708-8
PII: S 0002-9939(97)03708-8
Received by editor(s): October 23, 1995
Received by editor(s) in revised form: December 13, 1995
Communicated by: Palle E. Jørgensen
Article copyright: © Copyright 1997 American Mathematical Society