Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Morse index properties of colliding solutions to the $N$-body problem   We study a singular Hamiltonian system with an $\al$-homogeneous potential
that contains, as a particular case, the classical $N$--body problem. We
introduce a variational Morse--like index for a class of collision solutions
and, using the asymptotic estimates near collisions, we prove the
non-minimality of some special classes of colliding trajectories under suitable
spectral conditions provided $\al$ is sufficiently away from zero. We then
prove some minimality results for small values of the parameter $\al$.

26
The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
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The categories of this paper are: eess
7
The categories of this paper are: hep-th