The elusive Liapunov periodic solutions
type: Item
instance of: scholarly article
title: The elusive Liapunov periodic solutions
zbMATH Open document ID: 1342.34061
author: Kenneth R. Meyer
author: Jesús F. Palacián
author: Patricia Yanguas
published in: Qualitative Theory of Dynamical Systems
publication date: 2016-01-14T00:00:00Z
review text: The authors study the existence of families of periodic solutions for Hamiltonian systems when the classical Liapunov center theorem fails due to a resonance. In the proof, regular and singular reduction methods are used, together with classical perturbation theory. The starting point is the classic 1892 Liapunov center theorem and the test problem is a two-degree-of freedom Hamiltonian system in \(\mathbb{R}^4\) which is studied by a Hamiltonian system on a two dimensional real algebraic surface. Several examples are discussed in detail with graphical illustrations: resonance \(2:-1\), resonance \(3:-1\), resonance \(k:-1\), \(k \geq 4\) and resonance \(1:-1\).
reviewed by: Antonio Cañada
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 37J15
Mathematics Subject Classification ID: 37J40
zbMATH DE Number: 6529967
zbMATH Keywords: Hamiltonian systems, periodic solutions
zbMATH Keywords: Liapunov center theorem
zbMATH Keywords: resonance
zbMATH Keywords: regular reduction methods
zbMATH Keywords: singular reduction methods
zbMATH Keywords: classical perturbation theory
MaRDI profile type: Publication
full work available at URL: s12346-015-0134-3
OpenAlex ID: W2009587042
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DOI: 10.1007/S12346-015-0134-3
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description: scientific article; zbMATH DE number 6529967