Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Morse index and bifurcation for figure-eight choreographies of the equal
  mass three-body problem   We report on the Morse index and periodic solutions bifurcating from the
figure-eight choreography for the equal mass three-body problem under
homogeneous potential $-1/r^a$ for $a \ge 0$, and under Lennard-Jones (LJ) type
potential $1/r^{12}-1/r^6$, where $r$ is a distance between bodies. It is shown
that the Morse index changes at a bifurcation point and all solutions
bifurcating are approximated by variational functions responsible for the
change of the Morse index. Inversely we observed %numerically bifurcation
occurs at every point where the Morse index changes for the figure-eight
choreography under $-1/r^a$, and for $\alpha$ solution under LJ type potential,
where $\alpha$ solution is a figure-eight choreography tending to that under
$-1/r^6$ for infinitely large period. Thus, to our numerical studies, change of
the Morse index is not only necessary but also sufficient condition for
bifurcation for these choreographies. Further we observed that the change of
the Morse index is equal to the number of bifurcated solutions regarding
solutions with congruent orbits as the same solution.

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The categories of this paper are: nucl-ex
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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: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas