Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global planar dynamics with star nodes: beyond Hilbert's $16^{th}$
  problem   This is a complete study of the dynamics of polynomial planar vector fields
whose linear part is a multiple of the identity and whose nonlinear part is a
homogeneous polynomial. It extends previous work by other authors that was
mainly concerned with the existence and number of limit cycles. The general
results are also applied to two classes of examples where the nonlinearities
have degrees 2 and 3, for which we provide a complete set of phase portraits.

16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat