Shooting for the eight: A topological existence proof for a figure-eight orbit of the three-body problem

Richard B Moeckel

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

A topological existence proof is given for a figure-eight periodic solution of the equal mass three-body problem. The proof is based on the construction of a Wazewski set W in the phase space. The figure-eight solution is then found by a kind of shooting argument in which symmetrical initial conditions entering W are followed under the flow until they exit W. A linking argument shows that the image of the symmetrical entrance states under this flow map must intersect an appropriate set of symmetrical exit states.

Original languageEnglish (US)
Title of host publicationDifferential Equations
Subtitle of host publicationGeometry, Symmetries and Integrability - The Abel Symposium 2008, Proceedings of the 5th Abel Symposium
Pages287-310
Number of pages24
DOIs
StatePublished - Dec 1 2009
Event5th Abel Symposium 2008 - Differential Equations: Geometry, Symmetries and Integrability - Tromso, Norway
Duration: Jun 17 2008Jun 22 2008

Publication series

NameDifferential Equations: Geometry, Symmetries and Integrability - The Abel Symposium 2008, Proceedings of the 5th Abel Symposium

Other

Other5th Abel Symposium 2008 - Differential Equations: Geometry, Symmetries and Integrability
CountryNorway
CityTromso
Period6/17/086/22/08

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