Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Vlasov-Poisson equation, the Moebius Geometry and then-body problem
  in a negative space form   By using, the Vlasov-Poisson equation defined in either a Riemannian or a
semi-Riemannian space $\mathbb{R}^k_g$, and a Dirac distribution function, we
re-obtain the well known and classical equations of motion of a mechanical
system with a pairwise acting potential function. We apply this result to the
study of an $n$--body problem in a two dimensional negative space form with the
hyperbolic cotangent potential. Following the Klein's geometric Erlangen
program, with methods of M\"{o}bius geometry and using the Iwasawa
decomposition of the M\"{o}bius isometric group $SL(2,\mathbb{R})$ via its
representation in one Clifford Algebra, we complete the study of the whole set
of M\"{o}bius solutions (relative equilibria) of the problem begun by Diacu
{\it et al.} in \cite{Diacu8}.

15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
1
The categories of this paper are: cs
18
The categories of this paper are: econ