Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limit cycles for a class of quintic $\mathbb{Z}_6-$equivariant systems
  without infinite critical points   We analyze the dynamics of a 4-parameter family of planar ordinary
differential equations, given by a polynomial of degree 5 that is equivariant
under a symmetry of order 6. We obtain the number of limit cycles as a function
of the parameters, and provide criteria for proving in some cases uniqueness
and hyperbolicity of the limit cycle surrounding either 1, 7 or 13 critical
points, the origin being always one of these points. The method used is the
reduction of the problem to an Abel equation.

20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con