Volume 154, Number 1 (1999), in the article “Bridges between the Generalized Sitnikov Family and the Lyapunov Family of Periodic Orbits,” by Jaume Llibre, Kenneth R. Meyer, Jaume Soler, pages 140–156 ()

Bridges between the Generalized Sitnikov

Bridges between the Generalized Sitnikov Family and the Lyapunov Family of Periodic Orbits

✍ Jaume Llibre; Kenneth R. Meyer; Jaume Soler 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 138 KB

The linearization of the spatial restricted three body problem at the collinear equilibrium point L 2 has two pairs of pure imaginary eigenvalues and one pair of real eigenvalues so the center manifold is four dimensional. By the classical Lyapunov center theorem there are two families of periodic s