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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Isolating blocks near the collinear relative equilibria of the three-body problem


Author: Richard Moeckel
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 4395-4425
MSC (2000): Primary 70F10, 70F15, 37N05
Published electronically: January 23, 2004
MathSciNet review: 2067126
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Abstract: The collinear relative equilibrium solutions are among the few explicitly known periodic solutions of the Newtonian three-body problem. When the energy and angular momentum constants are varied slightly, these unstable periodic orbits become normally hyperbolic invariant spheres whose stable and unstable manifolds form separatrices in the integral manifolds. The goal of this paper is to construct simple isolating blocks for these invariant spheres analogous to those introduced by Conley in the restricted three-body problem. This allows continuation of the invariant set and the separatrices to energies and angular momenta far from those of the relative equilibrium.


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Additional Information

Richard Moeckel
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: rick@math.umn.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03418-X
PII: S 0002-9947(04)03418-X
Keywords: Celestial mechanics, central configurations, three-body problem
Received by editor(s): December 11, 2002
Received by editor(s) in revised form: May 7, 2003
Published electronically: January 23, 2004
Article copyright: © Copyright 2004 American Mathematical Society