Hamiltonian oscillators in \(1\)-\(1\)-\(1\) resonance: Normalization and integrability
type: Item
instance of: scholarly article
title: Hamiltonian oscillators in \(1\)-\(1\)-\(1\) resonance: Normalization and integrability
zbMATH Open document ID: 0974.34034
author: Patricia Yanguas
author: S. Ferrer
author: Jesús F. Palacián
published in: Journal of Nonlinear Science
publication date: 2000-05-07T00:00:00Z
review text: Here, a family of three degree of freedom Hamiltonian systems defined by a Taylor expansion around an elliptic equilibrium is considered. More precisely, the system is a perturbed harmonic oscillator in \(1-1-1\) resonance. The perturbation is an arbitrary polynomial with cubic and quartic terms in Cartesian coordinates. A second-order normal form using the invariants of the reduced phase space is obtained. The normal form is expressed in the invariants and in only six terms. By means of the nodal-Lissajous variables, relations are obtained among the parameters defining the perturbation, which lead to integrable subfamilies. Finally some applications are given.
reviewed by: Vasile Marinca
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 37J15
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 1439883
zbMATH Keywords: oscillators
zbMATH Keywords: resonances
zbMATH Keywords: reduction
zbMATH Keywords: symmetries
zbMATH Keywords: integrability
zbMATH Keywords: normal forms
zbMATH Keywords: invariants
zbMATH Keywords: Hamiltonian systems
MaRDI profile type: Publication
full work available at URL: s003329910007
OpenAlex ID: W2135331293
DOI: 10.1007/S003329910007
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description: scientific article; zbMATH DE number 1439883