On the problem of convexity for the restricted three-body problem around the heavy primary
The authors consider the energy surface of the planar rotating Kepler problem for energy below the first critical level. They show that, outside a small neighborhood of the collisions, there is a convex symplectic embedding of the double cover of the component of the energy surface around the heavy body into \({\mathbb R}^4\). This approach is relevant to attack the Birkhoff conjecture about the existence of a global surface of section in the restricted planar circular three-body problem using holomorphic curve techniques.
scientific article; zbMATH DE number 7608269
scientific article