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

2011/03/20 by Peter Albers, Joel W. Fish, Urs Frauenfelder +2 · 1 citation
Mathematics · #math.SG #math.DG #math.DS

paper · pdf · doi:10.1007/s00205-011-0475-2

published as Archive for Rational Mechanics and Analysis, (2012), 273-284 · 11 pages, 1 figure

arxiv created 2011/03/20 · arxiv updated 2012/08/13

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.

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