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Ergodicity, transitivity, and regularity for linear cellular automata over Zm

โœ Scribed by Gianpiero Cattaneo; Enrico Formenti; Giovanni Manzini; Luciano Margara

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
142 KB
Volume
233
Category
Article
ISSN
0304-3975

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โœฆ Synopsis

We study the dynamical behavior of D-dimensional linear cellular automata over Zm. We provide an easy-to-check necessary and su cient condition for a D-dimensional linear cellular automata over Z m to be ergodic and topologically transitive. As a byproduct, we get that for linear cellular automata ergodicity is equivalent to topological transitivity. Finally, we prove that for 1-dimensional linear cellular automata over Z m, regularity (denseness of periodic orbits) is equivalent to surjectivity.

๐Ÿ“œ SIMILAR VOLUMES

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We study the dynamical behavior of D-dimensional linear cellular automata over Zm. We provide easy-to-check necessary and sufficient conditions for a D-dimensional linear cellular automata over Zm to be sensitive to initial conditions, positively expansive, strongly transitive, and equicontinuous. A