Measure rigidity for algebraic bipermutative cellular automata

DOI10.1017/S0143385707000247zbMath1127.37017arXivmath/0510564OpenAlexW2017305420MaRDI QIDQ5436460

Mathieu Sablik

Publication date: 16 January 2008

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0510564

zbMATH Keywords

Haar measureBernoulli measureinvariant probability measure

Mathematics Subject Classification ID

Dynamical aspects of cellular automata (37B15) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items (6)

Percolation on the three dot system ⋮ On the Bernoulli automorphism of reversible linear cellular automata ⋮ Defect particle kinematics in one-dimensional cellular automata ⋮ Statistical mechanics of surjective cellular automata ⋮ Surjective cellular automata with zero entropy are almost one-to-one ⋮ The ergodic theory of cellular automata

Cites Work

• On Cesàro limit distribution of a class of permutative cellular automata
• Lyapunov exponents for one-dimensional cellular automata
• Combinatorial constructions associated to the dynamics of one-sided cellular automata.
• Uniform Bernoulli measure in dynamics of permutative cellular automata with algebraic local rules
• Expansive invertible onesided cellular automata
• Additive cellular automata and volume growth
• Isomorphism and measure rigidity for algebraic actions on zero-dimensional groups
• Invariant measures for bipermutative cellular automata
• Expansive dynamics on zero-dimensional groups
• Cellular automata and Lyapunov exponents
• Limit measures for affine cellular automata II
• Cesàro mean distribution of group automata starting from measures with summable decay
• Limit measures for affine cellular automata
• Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
• Endomorphisms and automorphisms of the shift dynamical system
• Subshifts of the three dot system

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