On the position of chaotic trajectories
type: Item
instance of: scholarly article
title: On the position of chaotic trajectories
zbMATH Open document ID: 1403.34036
author: Josef Diblík
author: Alessandro Calamai
author: Matteo Franca
author: Michal Pospíšil
published in: Journal of Dynamics and Differential Equations
publication date: 2018-01-26T00:00:00Z
review text: In this work, the authors locate trajectories of a perturbed system. Employing a Melnikov analysis they show that under certain conditions all the chaotic trajectories of the perturbed system lie in the same region, which is the main result of this study. Two examples are presented as applications to the results. In the first one they show how the results can be used in order to find positive radial solutions for some P.D.E. problems. Then they apply the results to a system of two coupled pendula and they find chaotic patterns without inversion of the motion.
reviewed by: Makrina Agaoglou
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 37G20
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 34E10
zbMATH DE Number: 6829887
zbMATH Keywords: Melnikov theory
zbMATH Keywords: dynamical system
zbMATH Keywords: bifurcation theory
zbMATH Keywords: chaotic behaviour
zbMATH Keywords: Hardy potential
zbMATH Keywords: Bernoulli shift
zbMATH Keywords: Melnikov integral
MaRDI profile type: Publication
full work available at URL: s10884-016-9520-z
OpenAlex ID: W2306821950
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DOI: 10.1007/S10884-016-9520-Z
description: scientific article; zbMATH DE number 6829887