Global surfaces of section in the planar restricted 3-body problem

Abstract

The restricted planar three-body problem has a rich history, yet many unanswered questions still remain. In the present paper we prove the existence of a global surface of section near the smaller body in a new range of energies and mass ratios for which the Hill's region still has three connected components. The approach relies on recent global methods in symplectic geometry and contrasts sharply with the perturbative methods used until now.

11 pages, 1 figure

References in corpus (2)

• The contact geometry of the restricted 3-body problem
• The Conley-Zehnder indices of the rotating Kepler problem

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• On the singular Weinstein conjecture and the existence of escape orbits for $b$-Beltrami fields
• Global surfaces of section for Reeb flows in dimension three and beyond
• Global diffusion on a tight three-sphere
• From Dynamics to Contact and Symplectic Topology and Back