Bifurcations of periodic solutions of Hamiltonian systems using fixed point methods
type: Item
instance of: scholarly article
title: Bifurcations of periodic solutions of Hamiltonian systems using fixed point methods
zbMATH Open document ID: 0883.58022
author: Kenneth R. Meyer
published in: Differential Equations and Dynamical Systems
publication date: 1997-05-28T00:00:00Z
review text: In this article the author studies the bifurcations of periodic solutions of periodic Hamiltonian systems on \(\mathbb{R}^4\) with two degrees of freedom depending on two parameters, say, \(\mu\) and \(\nu\). By analysing the 4-jet of the normal forms of the Hamiltonian systems, the author is able to find a region \(S\) in the \(\mu,\nu\)-parameter plane bounded by two smooth curves where bifurcations occur. It is proved that on the curves the system has at least two periodic solutions while in the region \(S\) there are at least three periodic solutions.
reviewed by: Marco A. Teixeira
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 1014352
zbMATH Keywords: bifurcations
zbMATH Keywords: periodic solutions
zbMATH Keywords: Hamiltonian systems
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1014352