A convex embedding for the rotating Kepler problem

Abstract

In this note, we prove that below the first critical energy level, a proper combination of the Ligon-Schaaf and Levi-Civita regularization mappings provides a convex symplectic embedding of the energy surfaces of the planar rotating Kepler problem into $R^4$ endowed with its standard symplectic structure. A direct consequence is the dynamical convexity of the planar rotating Kepler problem, which has been established by Albers-Fish-Frauenfelder-van Koert by direct computations. This result opens up new approaches 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.

10 pages

Cited by in corpus (2)

• On a convex embedding of the Euler problem of two fixed centers
• The symmetry of the Kepler problem, the inverse Ligon-Schaaf mapping and the Birkhoff conjecture