Bifurcation from a periodic orbit in perturbed planar Hamiltonian systems.
type: Item
instance of: scholarly article
title: Bifurcation from a periodic orbit in perturbed planar Hamiltonian systems.
zbMATH Open document ID: 1039.70012
DOI: 10.1016/S0022-247X(02)00504-8
author: Marc Henrard
author: Fabio Zanolin
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-04-09T00:00:00Z
review text: The authors study the perturbed plane differential system \(u'= -J\nabla H(u)+ p(\varepsilon, t,u)\). Here \(t\) is a variable, \(p\) is Carathéodory function, \(T\) is periodic in variable \(t\), and \(j\) is a symplectic matrix. \(T\)-periodic functions are looked for. Theorems are proved which give conditions for the existence of \(T\)-periodic solution. Some properties of the time map are discussed, and an application of periodic solutions close to the homoclinic ones is studied.
Mathematics Subject Classification ID: 70H09
Mathematics Subject Classification ID: 70K44
Mathematics Subject Classification ID: 70K50
zbMATH DE Number: 1895742
zbMATH Keywords: homoclinic trajectory
zbMATH Keywords: Carathéodory function
zbMATH Keywords: existence
zbMATH Keywords: \(T\)-periodic solution
zbMATH Keywords: time map
MaRDI profile type: Publication
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full work available at URL: s0022-247x(02)00504-8
OpenAlex ID: W2047684597
description: scientific article; zbMATH DE number 1895742