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

• Autorzy: Piotr Oprocha , Guohua Zhang
• Języki publikacji: EN

Abstrakty

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.

Kategorie tematyczne

• 37B40: Topological entropy
• 37E25: Maps of trees and graphs
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)
• 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 202
• Numer: 3
• Strony: 261-288

Daty

wydano

2011

Twórcy

autor

Piotr Oprocha

• 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

Guohua Zhang

• 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

Identyfikatory

DOI

10.4064/sm202-3-4