Archive for Rational Mechanics and Analysis

, Volume 204, Issue 1, pp 273–284 | Cite as

Global Surfaces of Section in the Planar Restricted 3-Body Problem

  • Peter Albers
  • Joel W. Fish
  • Urs Frauenfelder
  • Helmut Hofer
  • Otto van Koert


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.


Periodic Orbit Periodic Point Homoclinic Orbit Global Surface Symplectic Geometry 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Peter Albers
    • 1
  • Joel W. Fish
    • 2
  • Urs Frauenfelder
    • 4
  • Helmut Hofer
    • 3
  • Otto van Koert
    • 4
  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA
  2. 2.Department of MathematicsStanford UniversityStanfordUSA
  3. 3.Institute for Advanced StudyPrincetonUSA
  4. 4.Department of Mathematics and Research Institute of MathematicsSeoul National UniversitySeoulKorea

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