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Attractors in cellular automata

Published online by Cambridge University Press:  19 September 2008

Mike Hurley
Mike Hurley
Affiliation:
Department of Mathematics and Statistics, Case Western Reserve University, Cleveland, Ohio 44106, USA
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Abstract

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We give a classification theorem for cellular automata, showing that either there is a minimal quasi-attractor whose basin has full measure, or else no chain component has a basin with positive measure.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 1 , March 1990, pp. 131 - 140
Copyright
Copyright © Cambridge University Press 1990

References

REFERENCES

[1]Conley, C.. Isolated Invariant Sets and the Morse Index. Amer. Math. Soc.: Providence, 1978.CrossRefGoogle Scholar
[2]Denker, M., Grillenberger, C. & Sigmund, K.. Ergodic Theory on Compact Spaces. Springer Lect. Notes in Math., 527 Springer-Verlag: New York: 1976.CrossRefGoogle Scholar
[3]Farmer, D., Toffoli, T. & Wolfram, S.. Eds., Cellular automata: Proc. of an interdisciplinary workshop. Physica 10D (1, 2) (1984).Google Scholar
[4]Gilman, R.. Classes of linear automata. Ergod. Th. & Dynam. Sys. 7 (1987), 105–118;CrossRefGoogle Scholar
also, Periodic behavior of linear automata, pp. 216–219Google Scholar
in: Dynamical Systems. Lecture Notes in Mathematics 1342. Springer Verlag, New York, 1988.Google Scholar
[5]Hedlund, G.. Endomorphisms and automorphisms of the shift dynamical system. Math. Sys. Th. 3 (1969), 320–375.CrossRefGoogle Scholar
[6]Hurley, M.. Attractors: persistence, and density of their basins, Trans. Amer. Math. Soc. 269 (1982), 247–271.CrossRefGoogle Scholar
[7]Hurley, M., Generic properties of attractors in Euclidean spaces. Proc. of the Berkeley-Ames Conference on Nonlinear Problems in Control and Fluid Dynamics, pp. 283–298. Hunt, L. & Martin, C., eds. Math. Sci. Press: Brookline, Mass., 1984.Google Scholar
[8]Jen, E.. Invariant strings and pattern-recognizing properties of one-dimensional cellular automata. J. Stat. Phys 43 (1986), 243–265.CrossRefGoogle Scholar
[9]Milnor, J.. On the concept of attractor: correction and remarks. Commun. Math. Phys. 102 (1985), 517–519.CrossRefGoogle Scholar
[10]Wolfram, S.. Statistical mechanics of cellular automata. Rev. Mod. Phys. 55 (1983), 601–644.CrossRefGoogle Scholar
[11]Wolfram, S.. Universality and complexity in cellular automata. Physica 10D (1984), 1–35.Google Scholar