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On local aspects of topological weak mixing, sequence entropy and chaos

Published online by Cambridge University Press:  11 April 2013

PIOTR OPROCHA
Affiliation:
AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Kraków, Poland email oprocha@agh.edu.pl Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-956 Warszawa, Poland
GUOHUA ZHANG
Affiliation:
School of Mathematical Sciences and LMNS, Fudan University, Shanghai 200433, China email chiaths.zhang@gmail.com

Abstract

In this paper we show that for every $n\geq 2$ there are minimal systems with perfect weakly mixing sets of order $n$ and all weakly mixing sets of order $n+ 1$ trivial. We present some relations between weakly mixing sets and topological sequence entropy; in particular, we prove that invertible minimal systems with non-trivial weakly mixing sets of order three always have positive topological sequence entropy. We also study relations between weak mixing of sets and other well-established notions from qualitative theory of dynamical systems like (regional) proximality, chaos and equicontinuity in a broad sense.

Type
Research Article
Copyright
Copyright ©2013 Cambridge University Press 

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