Bifurcation of homoclinic orbits for Hamiltonian systems
type: Item
instance of: scholarly article
title: Bifurcation of homoclinic orbits for Hamiltonian systems
zbMATH Open document ID: 0780.58034
author: Salem Mathlouthi
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 1994-02-02T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73301
review text: The author considers a Hamiltonian ordinary differential equation imbedded in a dissipative family of nonautonomous differential equations depending periodically on the time. Otherwise a nonautonomous non- Hamiltonian perturbation of an autonomous Hamiltonian system is studied. It is supposed that the nonperturbed system admits a hyperbolic periodic solution and homoclinic solutions to such a periodic orbit. A necessary and sufficient condition of bifurcation in the perturbated system, is given (existence of doubly-asymptotic solutions). An asymptotic development of the bifurcated solution and two examples are presented. Since a long time this subject has been very popular in the research groups on ``Nonlinear Dynamics'' of the former Soviet Union. The author's references do not know this relatively ancient contribution.
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 37J40
zbMATH DE Number: 202537
zbMATH Keywords: nonlinear dynamics
zbMATH Keywords: bifurcation
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: homoclinic set
reviewed by: Christian Mira
MaRDI profile type: Publication
OpenAlex ID: W2322302464
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DOI: 10.5802/AFST.746
description: scientific article; zbMATH DE number 202537