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Zbl 0724.70015
Xia, Zhihong
Central configurations with many small masses. (English)
[J] J. Differ. Equations 91, No.1, 168-179 (1991). ISSN 0022-0396

Summary: By using the method of analytical continuation, we find the exact numbers of central configurations for some open sets of n positive masses for any choice of n. It turns out that the numbers increase dramatically as n increases; e.g., for some open set of 18 positive masses, some $2.08766\times 10\sp{20}$ classes of distinctive central configurations are found. In the mean time, we obtained some results about the Hausdorff measure for the set of n positive masses where degenerate central configuration arises.

MSC 2000:: *70G10 Generalized coordinates etc.
70F10 n-body problem
70-08 Computational methods (mechanics of particles and systems)

Keywords: method of analytical continuation; central configurations; Hausdorff measure

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