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April  2005, 13(1): 195-202. doi: 10.3934/dcds.2005.13.195

Homogeneity of surjective cellular automata

T.K. Subrahmonian Moothathu 1,

1. 

Department of Mathematics and Statistics, University of Hyderabad, Hyderabad 500046, India

Received  January 2004 Revised  December 2004 Published  March 2005

We bring out some similarities among one-dimensional surjective cellular automata. Four main results are the following: (i) all periodic points of a cellular automata are shift-periodic if and only if the set of periodic points of any fixed period is finite, (ii) forward recurrent points as well as backward recurrent points are residual for every onto cellular automata, (iii) every onto cellular automata is semi-open, and (iv) all transitive cellular automata are weak mixing and hence maximally sensitive (which improves an existing result).
Keywords: Cellular automata, recurrent point, sensitivity, transitivity, periodic point, weak mixing., semi-openness.
Mathematics Subject Classification: 54H20, 37B1.
Citation: T.K. Subrahmonian Moothathu. Homogeneity of surjective cellular automata. Discrete & Continuous Dynamical Systems, 2005, 13 (1) : 195-202. doi: 10.3934/dcds.2005.13.195
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