There exist one-dimensional transitive cellular automata with non-empty set of strictly temporally periodic points

• Autorzy: Matyja J.

Identyfikatory

DOI

10.4467/20838476SI.13.004.2089

• Języki publikacji: EN

Abstrakty

EN

In a Cantor metric space BZ; we present a one-sided cellular automaton which positively answers the question Does it exist a transitive cellular automaton (BZ; F) with non-empty set of strictly temporally periodic points? The question can be found in a current and recognized literature of the subject.

Słowa kluczowe

EN

one-dimensional cellular automata; transitive; strictly temporally; periodic points

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Schedae Informaticae
• Rocznik: 2013
• Tom: Vol. 22
• Strony: 41--45
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Matyja J.

• Silesian Technical University, Department of Computer Science and Econometrics, Roosevelta 26-28, 41-800 Zabrze, Poland

Bibliografia

• [1] Acerbi L., Dennunzio A., Formenti E.; Conservation of some dynamical properties for operations on cellular automata, Theoretical Computer Science 410,2009, pp. 3685-3693.
• [2] Banks J., Brooks J., Cairns G., Davis G., Stacey P.; On Devaney's definition of chaos, American Mathematical Monthly 99, 1992, pp. 332-334.
• [3] Blanchard F., Cervelle J., Formenti E.; Some results about the chaotic behavior of cellular automata, Theoretical Computer Science 349, 2005, pp. 318-336.
• [4] Blanchard F., Maass A.; Dynamical properties of expansive cellular automata, Israel Journal of Mathematics 99, 1997, pp. 149-174.
• [5] Boyle M., Kitchens B.; Periodic points for onto cellular automata, Indagationes Mathematicae 10, 1999, pp. 483-493.
• [6] Dennunzio A., Di Lena P., Formenti E., Margara L.; On the directional dynamics of additive cellular automata, Theoretical Computer Science 410, 2009, pp.4823-4833.
• [7] Dennunzio A., Di Lena P., Margara L.; Strictly temporally periodic points in cellular automata, Automata and JAC 2012, EPTCS 90, pp. 225-235.
• [8] Di Lena P.; On computing the topological entropy of one-sided cellular automata, Journal of Cellular Automata 2, 2007, pp. 121-130.
• [9] Di Lena P., Margara L.; Row subshifts and topological entropy of cellular automata, Journal of Cellular Automata 2, 2007, pp. 131-140.
• [10] Fory#s W., Matyja J., An example of one-sided, D-chaotic CA over four elementary alphabet, which is not E-chaotic and not injective, Journal of Cellular Automata 6, 2011, pp. 231-243.
• [11] Hedlund G.A.; Endomorphisms and automorphisms of the shift dynamical systems, Math. Systems Theory 3, 1969, pp. 320-375.
• [12] Kitchens B.P.; Symbolic dynamics: one-sided, two-sided and countable state Markov shifts, Springer-Verlag, Berlin 1998.
• [13] Kurka P.; Topological and symbolic dynamics, SMF, Cours Specialises, 2003.
• [14] Kurka P.; Topological dynamics of one-dimensional cellular automata, Encyclopedia of complexity and system sciences, Springer-Verlag, Berlin 2008.
• [15] Lind D., Marcus B.; An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, 1995.
• [16] Walters P.; An Introduction to Ergodic Theory, Springer-Verlag, New York 1982.