Stability and bifurcations of symmetric periodic orbits
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.
scientific article; zbMATH DE number 3976443
scientific article