Rosette Central Configurations, Degenerate Central Configurations and Bifurcations |
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Authors: | J Lei M Santoprete |
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Institution: | (1) Department of Mathematics, University of California, Irvine, CA, 92697, U.S.A.;(2) Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, 100084, China |
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Abstract: | In this paper we find a class of new degenerate central configurations and bifurcations in the Newtonian n-body problem. In particular we analyze the Rosette central configurations, namely a coplanar configuration where n particles of mass m1 lie at the vertices of a regular n-gon, n particles of mass m2 lie at the vertices of another n-gon concentric with the first, but rotated of an angle π /n, and an additional particle of mass m0 lies at the center of mass of the system. This system admits two mass parameters μ = m0/m1 and ε = m2/m1. We show that, as μ varies, if n > 3, there is a degenerate central configuration and a bifurcation for every ε > 0, while if n = 3 there is a bifurcation only for some values of ε. |
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Keywords: | bifurcations central configurations degenerate central configurations n-body problem |
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