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The Integral Manifolds of the Three Body Problem
Christopher K. McCord and Kenneth R. Meyer, University of Cincinnati, OH, and Quidong Wang, University of California, Los Angeles
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Memoirs of the American Mathematical Society
1998; 91 pp; softcover
Volume: 132
ISBN-10: 0-8218-0692-0
ISBN-13: 978-0-8218-0692-0
List Price: US$49 Individual Members: US$29.40
Institutional Members: US\$39.20
Order Code: MEMO/132/628

The phase space of the spatial three-body problem is an open subset in $${\mathbb R}^{18}$$. Holding the ten classical integrals of energy, center of mass, linear and angular momentum fixed defines an eight dimensional submanifold. For fixed nonzero angular momentum, the topology of this manifold depends only on the energy. This volume computes the homology of this manifold for all energy values. This table of homology shows that for negative energy, the integral manifolds undergo seven bifurcations. Four of these are the well-known bifurcations due to central configurations, and three are due to "critical points at infinity". This disproves Birkhoff's conjecture that the bifurcations occur only at central configurations.

• The analysis of $${\mathfrak K}(c,h)$$for equal masses
• The analysis of $${\mathfrak K}(c,h)$$ for general masses