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Rectangular orbits of the curved 4-body problem


Authors: Florin Diacu and Brendan Thorn
Journal: Proc. Amer. Math. Soc. 143 (2015), 1583-1593
MSC (2010): Primary 34C25, 37J45, 70F10
DOI: https://doi.org/10.1090/S0002-9939-2014-12326-4
Published electronically: November 4, 2014
MathSciNet review: 3314071
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Abstract: We consider the $ 4$-body problem in spaces of constant curvature and study the existence of spherical and hyperbolic rectangular solutions, i.e. equiangular quadrilateral motions on spheres and hyperbolic spheres. We
focus on relative equilibria (orbits that maintain constant mutual distances) and rotopulsators (configurations that rotate and change size, but preserve equiangularity). We prove that when such orbits exist, they are necessarily spherical or hyperbolic squares, i.e. equiangular equilateral quadrilaterals.


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Additional Information

Florin Diacu
Affiliation: Pacific Institute for the Mathematical Sciences, and Department of Mathematics and Statistics, University of Victoria, P.O. Box 1700 STN CSC, Victoria, BC, Canada V8W 2Y2
Email: diacu@uvic.ca

Brendan Thorn
Affiliation: Department of Mathematics and Statistics, University of Victoria, P.O. Box 1700 STN CSC, Victoria, BC, Canada V8W 2Y2
Email: bthorn@uvic.ca

DOI: https://doi.org/10.1090/S0002-9939-2014-12326-4
Received by editor(s): February 21, 2013
Received by editor(s) in revised form: July 30, 2013
Published electronically: November 4, 2014
Communicated by: Walter Craig
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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