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 | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-04-03418-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