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ERGODIC PROPERTIES OF CERTAIN SURJECTIVE CELLULAR AUTOMATA
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UNSPECIFIED (1992) ERGODIC PROPERTIES OF CERTAIN SURJECTIVE CELLULAR AUTOMATA. MONATSHEFTE FUR MATHEMATIK, 114 (3-4). pp. 305-316. ISSN 0026-9255.
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Abstract
We consider one-dimensional cellular automata, i.e. the maps T : P(Z) --> P(Z) (P is a finite wt with more than one element) which are given by (Tx)i = = F(x(i + l), ..., x(i + r)), x = (x(i)) (is-an-element-of Z) is-an-element-of P(Z) for some integers l less-than-or-equal-to r and a mapping F : P(r - l + 1) --> P. We prove that if F is right- (left-) permutative (in Hedlund's terminology) and 0 less-than-or-equal-to l < r (resp. l < r less-than-or-equal-to 0), then the natural extension of the dynamical system (P(Z), B, mu, T) is a Bernoulli automorphism (mu stands for the (1/p, ..., 1/p)-Bernoulli measure on the full shift P(Z)). If r < 0 or l > 0 and T is surjective, then the natural extension of the system (P(Z), B, mu, T) is a K-automorphism. We also prove that the shift Z2-action on a two-dimensional subshift of finite type canonically associated with the cellular automaton T is mixing, if F is both right and left permutative. These results answer some questions raised in [SR].
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | MONATSHEFTE FUR MATHEMATIK | ||||
Publisher: | SPRINGER-VERLAG WIEN | ||||
ISSN: | 0026-9255 | ||||
Official Date: | 1992 | ||||
Dates: |
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Volume: | 114 | ||||
Number: | 3-4 | ||||
Number of Pages: | 12 | ||||
Page Range: | pp. 305-316 | ||||
Publication Status: | Published |
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