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    政大機構典藏 > 理學院 > 應用數學系 > 期刊論文 >  Item 140.119/130199
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/130199

    Title: On the Quantitative Behavior of the Linear Cellular Automata.
    Authors: 班榮超
    Ban, Jung-Chao
    Akin, Hassan
    Chang, Chih-Hung
    Contributors: 應數系
    Keywords: Cellular automata;measure entropy;directional entropy;maximal measure
    Date: 2013-01
    Issue Date: 2020-06-22 13:42:21 (UTC+8)
    Abstract: In this paper, we study the quantitative behavior of one-dimensional linear cellular automata <[-r,r ], defined by local rule f (x-r , . . . , xr ) = �r i=-r λi xi (mod m), acting on the space of all doubly infinite sequences with values in a finite ring Zm, m ≥ 2. Once generalize the formulas given by Ban et al. [J. Cellular Automata 6 (2011) 385-397] for measure-theoretic entropy and topological pressure of one-dimensional cellular automata, we calculate the measure entropy and the topological pressure of the linear cellular automata with respect to the Bernoulli measure on the set ZZm. Also, it is shown that the uniform Bernoulli measure is the unique equilibrium measure for linear cellular automata. We compare values of topological entropy and topological directional entropy by using the formula obtained by Akın [J. Computation and Appl. Math. 225 (2) (2009) 459-466]. The topological directional entropy is interpreted by means of figures. As an application, we demonstrate that the Hausdorff of the limit set of a linear cellular automaton is the unique root of Bowen’s equation. Some open problems remain to be of interest.
    Relation: Journal of Cellular Automata, Vol.8, No.3-4, pp.205-231
    Data Type: article
    Appears in Collections:[應用數學系] 期刊論文

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