Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Periodic Solutions for Newtonian $n$-Body Problems with Dihedral
  Group Symmetry and Topological Constraints   In this paper, we prove the existence of a family of new non-collision
periodic solutions for the classical Newtonian $n$-body problems. In our
assumption, the $n=2l\geq4$ particles are invariant under the dihedral rotation
group $D_l$ in $\mathbb{R}^3$ such that, at each instant, the $n$ particles
form two twisted $l$-regular polygons. Our approach is variational minimizing
method and we show that the minimizers are collision-free by level estimates
and local deformations.

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The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph