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NCTS Seminar on Celestial Mechanics
14:30 - 15:20, March 15, 2018 (Thursday)
Lecture Room B, 4th Floor, The 3rd General Building, NTHU
(清華大學綜合三館 4樓B演講室)
Generic Finiteness of (n-2)-dimensional Central Configurations for Homogeneous Potentials with Integer Exponents (I)
Thiago Dias Oliveira Silva (National Tsing Hua University)


We present a polynomial parametrization for central configurations of dimension n -k. Also, we give a criterion for the dimension of an arbitrary central configuration in terms of the Cayley-Menger determinant. Finally, by using the Jacobian Criterion from Algebraic Geometry, we prove generic finiteness with respect to the masses for (n-2)-dimensional central configurations in the n-body problem under homogeneous potentials with integer exponents.


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