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On local aspects of topological weak mixing in dimension one and beyond

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Oprocha P., Zhang G.

Studia Mathematica

2011

tom 202

nr 3

261-288

We introduce the concept of weakly mixing sets of order n and show that, in contrast to weak mixing of maps, a weakly mixing set of order n does not have to be weakly mixing of order n + 1. Strictly speaking, we construct a minimal invertible dynamical system which contains a non-trivial weakly mixing set of order 2, whereas it does not contain any non-trivial weakly mixing set of order 3. In dimension one this difference is not that much visible, since we prove that every continuous map f from a topological graph into itself has positive topological entropy if and only if it contains a non-trivial weakly mixing set of order 2 if and only if it contains a non-trivial weakly mixing set of all orders.

Ograniczanie wyników

1 Studia Mathematica

1 Oprocha P.

1 Zhang G.

1 2011

Wyniki wyszukiwania

On local aspects of topological weak mixing in dimension one and beyond