A variational approach to chaotic dynamics in periodically forced nonlinear oscillators
type: Item
instance of: scholarly article
title: A variational approach to chaotic dynamics in periodically forced nonlinear oscillators
zbMATH Open document ID: 0978.37024
DOI: 10.1016/S0294-1449(00)00054-8
author: Elena Bosetto
author: Enrico Serra
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2002-02-13T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78505
review text: The authors prove that a class of problems containing the classical periodically forced pendulum equation displays the main features of chaotic dynamics. The approach is based on the construction of multi-bump type heteroclinic solutions to periodic orbits by the use of global variational methods. The use of the variational approach is often convenient because it does not require the system to be a small perturbation of a simpler one, needs in general only mild nondegeneracy conditions, and is powerful enough to detect the principal features of chaotic dynamics. The authors show that their results are in general valid for variational problems possessing two global minimizers, without assumptions on the space periodicity of the potential. On the other hand, the existence of consecutive minimizers is necessary in order to obtain multibump solutions.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 70K44
zbMATH DE Number: 1558336
zbMATH Keywords: chaotic dynamics
zbMATH Keywords: heteroclinic solutions
zbMATH Keywords: periodic orbits
zbMATH Keywords: variational approach
reviewed by: George S. Stavrakakis
MaRDI profile type: Publication
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OpenAlex ID: W2044494336
Wikidata QID: Q127647106
description: scientific article; zbMATH DE number 1558336