Splendid isolation: local uniqueness of the centered co-circular relative equilibria in the <Emphasis Type="Italic">N</Emphasis>-body problem |
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| Authors: | Email author" target="_blank">Marshall?HamptonEmail author |
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| Institution: | 1.Department of Mathematics and Statistics,University of Minnesota, Duluth,Duluth,USA |
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| Abstract: | We study the neighborhood of the equal mass regular polygon relative equilibria in the N-body probem, and show that this relative equilibirum is isolated among the co-circular configurations (in which each point lies on a common circle) for which the center of mass is located at the center of the common circle. It is also isolated in the sense that a sufficiently small mass cannot be added to the common circle to form a \(N+1\)-body relative equilibrium. These results provide strong evidence for a conjecture that the equal mass regular polygon is the only co-circular relative equilibrium with its center of mass located at the center of the common circle. |
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