Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Index Theory for Collision, Parabolic and Hyperbolic Solutions of the
  Newtonian $n$-body Problem   In the Newtonian $n$-body problem for solutions with arbitrary energy, which
start and end either at a total collision or a parabolic/hyperbolic infinity,
we prove some basic results about their Morse and Maslov indices. Moreover for
homothetic solutions with arbitrary energy, we give a simple and precise
formula that relates the Morse indices of these homothetic solutions to the
spectra of the normalized potential at the corresponding central
configurations. Potentially these results could be useful in the application of
non-action minimization methods in the Newtonian $n$-body problem.

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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn