Distributional chaos via isolating segments

Piotr Oprocha; Pawel Wilczynski

doi:10.3934/dcdsb.2007.8.347

Article Contents

2007, Volume 8, Issue 2: 347-356. Doi: 10.3934/dcdsb.2007.8.347

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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

Received: July 31, 2006

Revised: December 31, 2006

Published: August 2007

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Abstract

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 $0<\kappa \leq 0.5044$.

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Mathematics Subject Classification: Primary: 34C28; Secondary: 37B30.

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