Factor maps and invariant distributional chaos

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:256

Article

Forys, Magdalena^1,2  Oprocha, Piotr^1,3  Wilczynski, Pawel⁴ 

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

[2] Jagiellonian Univ, Inst Comp Sci, Fac Math & Comp Sci, PL-30348 Krakow, Poland

[3] Polish Acad Sci, Inst Math, PL-00956 Warsaw, Poland

[4] Warsaw Univ Technol, Fac Math & Informat Sci, PL-00662 Warsaw, Poland

关键词: Distributional chaos;    Invariant scrambled set;    Poincare map;    Factor map;    Symbolic dynamics;   

DOI  :  10.1016/j.jde.2013.09.009

来源: Elsevier

【 摘 要 】

The main aim of this article is to show that maps with the specification property have invariant distributionally scrambled sets and that this kind of scrambled set can be transferred from factor to extension under finite-to-one factor maps. This solves some open questions in the literature of the topic. We also show how our method can be applied in practice, taking as example Poincare map of time-periodic nonautonomous planar differential equation (z) over dot = v(t, z) = (1 + e(i kappa t)vertical bar z vertical bar(2))(z) over bar (3) - N where kappa and N are sufficiently small positive real numbers. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free