Measure rigidity for algebraic bipermutative cellular automata
نویسنده
چکیده
Let (AZ, F ) be a bipermutative algebraic cellular automaton. We present conditions which force a probability measure which is invariant for the N×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 AZ. This generalizes simultaneously results of B. Host, A. Maass and S. Mart́ınez [7] and M. Pivato [14]. This result is applied to give conditions which also force a (F,σ)-invariant probability measure to be the uniform Bernoulli measure when F is a particular invertible expansive cellular automaton on AN.
منابع مشابه
The ergodic theory of cellular automata
2 Invariant measures for CA 5 2A The uniform measure vs. surjective cellular automata . . . . . . . . . . . . 5 2B Invariance of maxentropy measures . . . . . . . . . . . . . . . . . . . . . . 8 2C Periodic invariant measures . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2D Posexpansive and permutative CA . . . . . . . . . . . . . . . . . . . . . . 10 2E Measure rigidity in algebraic C...
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