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On the Rotatıon Entropy of Additive Cellular Automata f_∞
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Volume 3, 2015
Issue 3 (June)
Pages: 70-73   |   Vol. 3, No. 3, June 2015   |   Follow on         
Paper in PDF Downloads: 16   Since Aug. 28, 2015 Views: 1698   Since Aug. 28, 2015
Bunyamin Aydin, Necmettin Erbakan University, Education of Faculty, Konya, Turkey.
In this paper, we first introduce the definition of rotational sets for cellular automata f_∞ using Misiurewicz’s rotational sets. After that, we define rotational entropy functions for cellular automata f_∞ from Bowen’s definiton of rotational entropy. Finally, we compare rotational entropy function with topologic entropy function for cellular automata f_∞.
Rotation Entropy, Topological Entropy, Cellular Automata
Botelho,F.(1991). Rotattion Entropy for annulus homeomorhphisms, Pacific J. Math., 132: 1-19.
Misiurewicz,M. and Ziemian,K.(1989). Rotationses for maps of tori, J. London Math. Soc. 40 (2): 490-506.
Poincare ́, H. Oeuvres completes, tomeİ (Gauthier-Villars, Paris, 1952) ,pp.137-158.
Fanks, J. (1988). Recurence and fixed point of surface homeomorphisms, Ergodiv Theory and Dynamical System, 8: 99-108.
Kim,S., Mackay,R.S. and Guckenheimer,J.(1989). Resonance regions for families of the torus maps, Nonlinearity 2: 391-404.
Hedlund,G.A.(1969). Endomorphisms and automorphisms of full shift dynamical system. Math. Syst. Theor. 3: 320-375.
Akın,H. (2003).On the Measure Entropy of Additive Cellular Automata f_∞, Entropy 5:233-238.
Cattaneo,G., Formenti,E., Manzini, G. and Margara,L.(2000). Ergodicity, transitivity, and regularity for linear cellular automata over Z^m , Theoret. Comput. Sci. 233 :147-164.
Shereshevsky, M.A. (1992). Ergodic properties of certain surjective cellular automata, Mh. Math. 114 : 305-316.
Botelho,F.(1988). Rotation sets for annulus homeomorhphisms, Pacific J. Math., 132: 251-266.
R.Bowen, Invariant measures for makov maps of the interval. Comm Math Physics, 1976, 69: 1-17.
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