Limit measures for affine cellular automata
نویسندگان
چکیده
منابع مشابه
Limit Measures for Affine Cellular Automata II
If M is a monoid, and A is an abelian group, then A is a compact abelian group; a linear cellular automaton (LCA) is a continuous endomorphism F : A −→ A that commutes with all shift maps. If F is diffusive, and μ is a harmonically mixing (HM) probability measure on A, then the sequence {Fμ}N=1 weak*-converges to the Haar measure on A, in density. Fully supported Markov measures on A are HM, an...
متن کاملLimit Measures for Affine Cellular Automata
Let M be a monoid (e.g. N, Z, or Z), and A an abelian group. A is then a compact abelian group; a linear cellular automaton (LCA) is a continuous endomorphism F : A −→ A that commutes with all shift maps. Let μ be a (possibly nonstationary) probability measure on A; we develop sufficient conditions on μ and F so that the sequence {Fμ}N=1 weak*-converges to the Haar measure on A, in density (and...
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Let M be a monoid (e. is then a compact abelian group; a linear cellular automaton (LCA) is a continuous endomorphism F : A M ?! A M that commutes with all shift maps. Let be a (possibly nonstationary) probability measure on A M ; we develop suucient conditions on and F so that the sequence fF N g 1 N=1 weak*-converges to the Haar measure on A M , in density (and thus, in Cess aro average as we...
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A right-sided, nearest neighbour cellular automaton (RNNCA) is a continuous transformation Φ : A−→A determined by a local rule φ : A{0,1}−→A so that, for any a ∈ A and any z ∈ Z, Φ(a)z = φ(az, az+1). We say that Φ is bipermutative if, for any choice of a ∈ A, the map A ∋ b 7→ φ(a, b) ∈ A is bijective, and also, for any choice of b ∈ A, the map A ∋ a 7→ φ(a, b) ∈ A is bijective. We characterize ...
متن کاملCommutators of Bipermutive and Affine Cellular Automata
We discuss bipermutive cellular automata from a combinatorial and topological perspective. We prove a type of topological randomizing property for bipermutive CA, show that the commutator of a bipermutive CA is always small and that bipermutive affine CA have only affine CA in their commutator. We show the last result also in the multidimensional case, proving a conjecture of [Moore-Boykett, 97].
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2002
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385702000548