The Generic Limit Set of Cellular Automata

被引：0
作者：
Djenaoui, Saliha [1 ,2 ]
Guillon, Pierre [1 ,3 ]
机构：
[1] Univ Aix Marseille, CNRS, Cent Marseille, I2M,UMR 7373, F-13453 Marseille, France
[2] Univ Badji Mokhtar Annaba, Dept Math, BP 12, Sidi Amar 23220, Annaba, Algeria
[3] Independent Univ Moscow, Interdisciplinary Sci Ctr JV Poncelet ISCP, CNRS, UMI 2615, Moscow, Russia
来源：
JOURNAL OF CELLULAR AUTOMATA | 2019年 / 14卷 / 5-6期
关键词：
Cellular automata; basin of attraction; limit set; attractor; directional dynamics; Baire category; symbolic dynamics; COMPUTATIONAL-COMPLEXITY; ATTRACTORS;
D O I：
暂无
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In topological dynamics, the generic limit set is the smallest closed subset which has a comeager realm of attraction. We study some of its topological properties, and the links with equicontinuity and sensitivity. We emphasize the case of cellular automata, for which the generic limit set is included in all subshift attractors, and discuss directional dynamics, as well as the link with measure-theoretical similar notions.
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收藏
页码：435 / 477
页数：43
相关论文
共 25 条
[1]   Conservation of some dynamical properties for operations on cellular automata [J].
Acerbi, Luigi ;
Dennunzio, Alberto ;
Formenti, Enrico .
THEORETICAL COMPUTER SCIENCE, 2009, 410 (38-40) :3685-3693
[2]  
[Anonymous], 1969, MATH SYST THEORY, DOI DOI 10.1007/BF01691062
[3]  
Bowen R., 1970, P S PURE MATH, V14, P23
[4]   μ-Limit sets of cellular automata from a computational complexity perspective [J].
Boyer, L. ;
Delacourt, M. ;
Poupet, V. ;
Sablik, M. ;
Theyssier, G. .
JOURNAL OF COMPUTER AND SYSTEM SCIENCES, 2015, 81 (08) :1623-1647
[5]   ON THE LIMIT-SETS OF CELLULAR AUTOMATA [J].
CULIK, K ;
PACHL, J ;
YU, S .
SIAM JOURNAL ON COMPUTING, 1989, 18 (04) :831-842
[6]  
de Vries Jan, 2014, GRUYTER STUDIES MATH
[7]   Directional dynamics along arbitrary curves in cellular automata [J].
Delacourt, M. ;
Poupet, V. ;
Sablik, M. ;
Theyssier, G. .
THEORETICAL COMPUTER SCIENCE, 2011, 412 (30) :3800-3821
[8]  
Delacourt Martin, 2011, AUTOMATES CELLULAIRE
[9]   Computational complexity of dynamical systems: The case of cellular automata [J].
Di Lena, P. ;
Margara, L. .
INFORMATION AND COMPUTATION, 2008, 206 (9-10) :1104-1116
[10]  
Durand B., 1994, Complex Systems, V8, P419
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