Isolating blocks near the collinear relative equilibria of the three-body problem
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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.References
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Additional Information
- Richard Moeckel
- Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
- Email: rick@math.umn.edu
- Received by editor(s): December 11, 2002
- Received by editor(s) in revised form: May 7, 2003
- Published electronically: January 23, 2004
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 356 (2004), 4395-4425
- MSC (2000): Primary 70F10, 70F15, 37N05
- DOI: https://doi.org/10.1090/S0002-9947-04-03418-X
- MathSciNet review: 2067126