Stability and bifurcations of symmetric periodic orbits
type: Item
instance of: scholarly article
title: Stability and bifurcations of symmetric periodic orbits
zbMATH Open document ID: 0604.70047
DOI: 10.1007/BF02850693
author: Andrea Milani
publication date: 1985-01-01T00:00:00Z
review text: Periodic orbits are important in the study of non-integrable Hamiltonian systems. In this paper a symmetric Hamiltonian system defined by \(H=H_ 0+\mu R\) is studied, where \(H_ 0\) defines an integrable system, and \(\mu\) is a small quantity. The paper starts from the classical continuation method and the more recent methods of the Morse theory and of the catastrophe theory of R. Thom are also used. Some conclusions about the existence and also the stability and the bifurcation of the symmetric periodic orbits are established. The restricted three-body problem is treated as an example.
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 70F07
zbMATH DE Number: 3976443
zbMATH Keywords: Periodic orbits
zbMATH Keywords: non-integrable Hamiltonian systems
zbMATH Keywords: symmetric Hamiltonian system
zbMATH Keywords: integrable system
zbMATH Keywords: classical continuation method
zbMATH Keywords: Morse theory
zbMATH Keywords: catastrophe theory
zbMATH Keywords: stability
zbMATH Keywords: bifurcation
zbMATH Keywords: symmetric periodic orbits
zbMATH Keywords: restricted three-body problem
reviewed by: Fuhua Ling
MaRDI profile type: Publication
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published in: Rendiconti del Circolo Matematico di Palermo
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description: scientific article; zbMATH DE number 3976443