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2011 | 202 | 3 | 261-288
Tytuł artykułu

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

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EN
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EN
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.
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  • Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain
  • Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland
autor
  • School of Mathematical Sciences and LMNS, Fudan University, Shanghai 200433, China
  • School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
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bwmeta1.element.bwnjournal-article-doi-10_4064-sm202-3-4
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