Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Inverse Problem for Nested Polygonal Relative Equilibria   We prove that for some potentials (including the Newtonian one, and the
potential of Helmholtz vortices in the plane) relative equilibria consisting of
two homothetic regular polygons of arbitrary size can only occur if the masses
at each polygon are equal. The same result is true for many regular polygons as
long as the ratio between the radii of the polygons are sufficient large.
Moreover, under these hypotheses, the relative equilibrium always exist.

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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci