Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An existence proof of a symmetric periodic orbit in the octahedral
  six-body problem   We present a proof of the existence of a periodic orbit for the Newtonian
six-body problem with equal masses. This orbit has three double collisions each
period and no multiple collisions. Our proof is based on the minimization of
the Lagrangian action functional on a well chosen class of symmetric loops.

8
The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs