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

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

doi:10.1007/s00205-011-0475-2

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

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

Mathematics

Purdue University
Stanford University
Seoul National University
Institute for Advanced Studies

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	273-284
Number of pages	12
Journal	Archive for Rational Mechanics and Analysis
Volume	204
Issue number	1
DOIs	https://doi.org/10.1007/s00205-011-0475-2
State	Published - Apr 2012

ASJC Scopus Subject Areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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10.1007/s00205-011-0475-2

Cite this

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

Abstract

ASJC Scopus Subject Areas

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