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September  2007, 8(2): 347-356. doi: 10.3934/dcdsb.2007.8.347

Distributional chaos via isolating segments

Piotr Oprocha 1, and  Pawel Wilczynski 2,

1. 

Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków
2. 

Institute of Mathematics, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland

Received  August 2006 Revised  January 2007 Published  June 2007

Recently, Srzednicki and Wójcik developed a method based on Wazewski Retract Theorem which allows, via construction of so called isolating segments, a proof of topological chaos (positivity of topological entropy) for periodically forced ordinary differential equations. In this paper we show how to arrange isolating segments to prove that a given system exhibits distributional chaos. As an example, we consider planar differential equation

ż$=(1+e^{i \kappa t}|z|^2)\bar{z}$

for parameter values $0<\kappa \leq 0.5044$.

Keywords: distributional chaos, isolating segments, fixed point index..
Mathematics Subject Classification: Primary: 34C28; Secondary: 37B3.
Citation: Piotr Oprocha, Pawel Wilczynski. Distributional chaos via isolating segments. Discrete & Continuous Dynamical Systems - B, 2007, 8 (2) : 347-356. doi: 10.3934/dcdsb.2007.8.347
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