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- W2053297396 abstract "The bifurcation of central configuration in the Newtonian N-body problem for any odd number N ≥ 7 is shown. We study a special case where 2n particles of mass m on the vertices of two different coplanar and concentric regular n-gons (rosette configuration) and an additional particle of mass m0 at the center are governed by the gravitational law he 2n+1 body problem. This system is of two degrees of freedom and permits only one mass parameter μ =m 0/m. This parameter μ controls the bifurcation. If n≥ 3, namely any odd N ≥ 7, then the number of central configurations is three when μ ≥ μ c , and one when μ ≥ μ c . By combining the results of the preceding studies and our main theorem, explicit examples of bifurcating central configuration are obtained for N ≤ 13, for any odd N ∈ [15,943], and for any N ≥ 945." @default.
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- W2053297396 date "2004-11-01" @default.
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- W2053297396 title "Bifurcation of central configuration in the 2N+1 body problem" @default.
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- W2053297396 doi "https://doi.org/10.1007/s10569-004-1991-2" @default.
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