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UNSPECIFIED (1992) ERGODIC PROPERTIES OF CERTAIN SURJECTIVE CELLULAR AUTOMATA. MONATSHEFTE FUR MATHEMATIK, 114 (34). pp. 305316.
Research output not available from this repository, contact author.Abstract
We consider onedimensional 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)) (isanelementof Z) isanelementof P(Z) for some integers l lessthanorequalto 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 lessthanorequalto l < r (resp. l < r lessthanorequalto 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 Kautomorphism. We also prove that the shift Z2action on a twodimensional 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  

Subjects:  Q Science > QA Mathematics  
Journal or Publication Title:  MONATSHEFTE FUR MATHEMATIK  
Publisher:  SPRINGERVERLAG WIEN  
ISSN:  00269255  
Official Date:  1992  
Dates: 


Volume:  114  
Number:  34  
Number of Pages:  12  
Page Range:  pp. 305316  
Publication Status:  Published 
Data sourced from Thomson Reuters' Web of Knowledge
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