Equality of Measure and Topological Entropies for Cellular Automata

• Autorzy: Foryś W. , Matyja J.
• Języki publikacji: EN

Abstrakty

EN

In the paper we consider cellular automata defined on metric spaces (AN, d) or (AZ, d) endowed with the uniform Bernoulli measure ž and present general constructions of such automata which are sur- jective, not positively expansive and ž is the measure of the maximal and positive entropy.

Słowa kluczowe

EN

infinite word; uniform Bernoulli measure; surjective cellular automata; entropy; dynamical system

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Schedae Informaticae
• Rocznik: 2006
• Tom: Vol. 15
• Strony: 151--164
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Foryś W.

autor

Matyja J.

• Jagiellonian University, Institute of Computer Science Nawojki 11, 30-027 Kraków, Poland,

Bibliografia

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• [2] Blanchard F., Kurka P., Maass A.; Topological and Measure-Theoretic Properties of One-Dimensional Cellular Automata, Physica D, 103, 1997, pp. 86-89.
• [3] Blanchard F., Maass A.; Dynamical Properties of Expansive Cellular Automata, Israel Journal of Mathematics, 99, 1997, pp. 149-174.
• [4] Brin M., Stuck G.; Introduction to Dynamical Systems, Cambridge University Press, 2002.
• [5] Goodwyn L.W.; Topological Entropy Bounds Measure-Theoretic Entropy, Proc.Amer. Math. Soc., 23, 1969, pp. 679-688.
• [6] Kurka P.; Languages, Equicontinuity and Attractors in Cellular Automata, Ergodic Theory Dynamical Systems, 17, 1997, pp. 417-433.
• [7] Kurka P.; Topological and Symbolic Dynamics, SMF, Cours Specialises, 2003.
• [8] Rudin W.; Real and Complex Analysis, McGraw-Hill, 1966.Received April 24, 2006