Singularities of planar symmetric four-body problems

Date

2010-01-08T22:03:06Z

Authors

Diacu, Florin N.

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Abstract

We first show that trapezoidal and rhomboidal solutions of the four-body problem with equal masses, do not lead to non-collision singularities and that any orbit encounters a collision, forwards or backwards in time. The existence of square homothetic solutions on negative energy levels, as connecting orbits between equilibria, is further proved and a transversality theorem, interpreted as a structure stability result, follows. Using McGehee transformations the total collapse singularity is blown up and the binary collisions are regularized. Finally we discuss the block-regularization of quadruple collision orbits as it follows from the qualitative behavior of the flow on the collision manifold.

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