Motion close to the Hopf bifurcation of the vertical family of periodic orbits of \(L_{4}\)
The authors investigate the vertical family of periodic orbits of triangular points \(L_4\) and \(L_5\) in spatial circular restricted three-body problem. The authors concentrate on the case \(\mu >\mu_R\), but close to \(\mu_R\) (the Routh critical mass parameter). The motions related to the Hopf bifurcation of the vertical family which appears if the mass parameter \(\mu>\mu_R\) are considered and investigated. A special attention is paid to the family with large enough amplitudes. The authors also examine periodic orbits, 2D and 3D invariant tori, and unstable and stable invariant manifolds for hyperbolic periodic orbits.
scientific article; zbMATH DE number 2139793