Multiplicative Cellular Automata on Nilpotent Groups: Structure, Entropy, and Asymptotics
نویسنده
چکیده
If M = ZD, and B is a finite (nonabelian) group, then B is a compact group; a multiplicative cellular automaton (MCA) is a continuous transformation G : B−→ B which commutes with all shift maps, and where nearby coordinates are combined using the multiplication operation of B. We characterize when MCA are group endomorphisms of B, and show that MCA on B inherit a natural structure theory from the structure of B. We apply this structure theory to compute the measurable entropy of MCA, and to study convergence of initial measures to Haar measure.
منابع مشابه
Nonabelian Multiplicative Cellular Automata
If M = Z, and G is a finite (nonabelian) group, then G is a compact group; a multiplicative cellular automaton (MCA) is a continuous transformation F : G − ←⊃ which commutes with all shift maps, and where nearby coordinates are combined together using the multiplication operator of G. We provide equivalent conditions for MCA to be group endomorphisms of G, and show how MCA on G inherit a natura...
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