## Orbits Near Triple Collision in the Three-body Problem |

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### Contents

Angular Equations | 4 |

The Case of Nonzero Angular Momentum | 8 |

The Collision Manifold | 15 |

5 other sections not shown

### Common terms and phrases

analytic curve analytic function analytic submanifold approach collision behavior of orbits binary exchange orbits branch of Un(E choose coordinates close to collision close to equal close to triple codimension collinear configurations collinear submanifold collision manifold components configuration space consisting of orbits continuous function crosses St(C denote Devaney double collision duals occur ejection orbit energy h equal masses equations 2.1 equilateral configurations following result gradient-like property homeomorphic homotopy equivalence intersect invariant manifold invariant submanifold ir(a isosceles orbit isosceles problem isosceles submanifold Lemma mass ratio masses sufficiently close McGehee neighborhood non-degenerate masses non-trivial open sets orbit segment ORBITS NEAR TRIPLE orbits which approach particles Proof of 7.1 proof of Proposition Proposition 6.4 Proposition 7.1 quotient rest points singular points subset sufficiently small Sundman Sundman's Inequality thesis three-body problem topological triple collision Un(C Un(P UNIVERSITY OF WISCONSIN-MADISON unstable manifolds unstarred sets variation of 9 vr shows