Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free time minimizers for the planar three-body problem   Free time minimizers of the action (called"semi-static" solutions by Ma\~ne)
play a central role in the theory of weak KAM solutions to the Hamilton-Jacobi
equation (see Fathi). We prove that any solution to Newton's three-body problem
which is asymptotic to Lagrange's parabolic homothetic solution is eventually a
free time minimizer. Conversely, we prove that every free time minimizer tends
to Lagrange's solution, provided the mass ratios lie in a certain large open
set of mass ratios. We were inspired by the work of Da Luz-Maderna who had
shown that every free time minimizer for the N-body problem is parabolic, and
therefore must be asymptotic to the set of central configurations. We exclude
being asymptotic to Euler's central configurations by a second variation
argument. Central configurations correspond to rest points for the McGehee
blown-up dynamics. The large open set of mass ratios are those for which the
linearized dynamics at each Euler rest point has a complex eigenvalue.

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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys