Distributionally chaotic systems of type 2 and rigidity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:452

Article

Forys-Krawiec, Magdalena^1,2  Oprocha, Piotr^1,2  Stefankova, Marta³ 

[1] AGH Univ Sci & Technol, Fac Appl Math, Al Mickiewicza 30, PL-30059 Krakow, Poland

[2] Div Univ Ostrava, Natl Supercomp Ctr IT4Innovat, Inst Res & Applicat Fuzzy Modeling, 30 Dubna 22, Ostrava 70103, Czech Republic

[3] Silesian Univ, Math Inst, Opava 74601, Czech Republic

关键词: Uniformly rigid;    Distributional chaos;    DC2;    Transitive;    Hilbert cube;   

DOI  :  10.1016/j.jmaa.2017.02.056

来源: Elsevier

【 摘 要 】

In this paper we deal with uniformly rigid systems obtained by a method introduced by Katznelson and Weiss and show that such systems never contain DC2 pairs. On the other hand, we introduce a modification of this technique that leads to a uniformly rigid system with DC2 pairs. We also show that every dynamical system contains a pair of distinct points which is not DC2. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free