Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing necessary integrability conditions for planar parametrized
  homogeneous potentials   Let $V\in\mathbb{Q}(i)(\a_1,\dots,\a_n)(\q_1,\q_2)$ be a rationally
parametrized planar homogeneous potential of homogeneity degree $k\neq -2, 0,
2$. We design an algorithm that computes polynomial \emph{necessary} conditions
on the parameters $(\a_1,\dots,\a_n)$ such that the dynamical system associated
to the potential $V$ is integrable. These conditions originate from those of
the Morales-Ramis-Sim\'o integrability criterion near all Darboux points. The
implementation of the algorithm allows to treat applications that were out of
reach before, for instance concerning the non-integrability of polynomial
potentials up to degree $9$. Another striking application is the first complete
proof of the non-integrability of the \emph{collinear three body problem}.

11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin