Topological Weak Mixing and Quasi-bohr Systems
نویسنده
چکیده
A minimal dynamical system (X,T ) is called quasi-Bohr if it is a nontrivial equicontinuous extension of a proximal system. We show that if (X,T ) is a minimal dynamical system which is not weakly mixing then some minimal proximal extension of (X, T ) admits a nontrivial quasi-Bohr factor. (In terms of Ellis groups the corresponding statement is: AG′ = G implies weak mixing.) The converse does not hold. In fact there are nontrivial quasi-Bohr systems which are weakly mixing of all orders. Our main tool in the proof is a theorem, of independent interest, which enhances the general structure theorem for minimal systems.
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