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- W2017305420 abstract "Abstract Let $({mathcal {A}^{mathbb {Z}}} ,F)$ be a bipermutative algebraic cellular automaton. We present conditions that force a probability measure, which is invariant for the $ {mathbb {N}} times {mathbb {Z}} $ -action of F and the shift map σ , to be the Haar measure on Σ, a closed shift-invariant subgroup of the abelian compact group $ {mathcal {A}^{mathbb {Z}}} $ . This generalizes simultaneously results of Host et al (B. Host, A. Maass and S. Martínez. Uniform Bernoulli measure in dynamics of permutative cellular automata with algebraic local rules. Discrete Contin. Dyn. Syst. 9 (6) (2003), 1423–1446) and Pivato (M. Pivato. Invariant measures for bipermutative cellular automata. Discrete Contin. Dyn. Syst. 12 (4) (2005), 723–736). This result is applied to give conditions which also force an ( F , σ )-invariant probability measure to be the uniform Bernoulli measure when F is a particular invertible affine expansive cellular automaton on $ {mathcal {A}^{mathbb {N}}} $ ." @default.
- W2017305420 created "2016-06-24" @default.
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- W2017305420 date "2007-12-01" @default.
- W2017305420 modified "2023-10-18" @default.
- W2017305420 title "Measure rigidity for algebraic bipermutative cellular automata" @default.
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- W2017305420 doi "https://doi.org/10.1017/s0143385707000247" @default.
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