Singularities of planar symmetric four-body problems

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dc.contributor.authorDiacu, Florin N.
dc.date.accessioned2010-01-08T22:03:06Z
dc.date.available2010-01-08T22:03:06Z
dc.date.copyright1991en
dc.date.issued2010-01-08T22:03:06Z
dc.description.abstractWe 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.en
dc.identifier.urihttp://hdl.handle.net/1828/2055
dc.language.isoenen
dc.relation.ispartofseriesDMS-591-IRen
dc.subjecttechnical reports (mathematics and statistics)
dc.subject.departmentDepartment of Mathematics and Statistics
dc.titleSingularities of planar symmetric four-body problemsen
dc.typeTechnical Reporten

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