Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Realization problems for limit cycles of planar polynomial vector fields   We show that for any finite configuration of closed curves $\Gamma\subset
\mathbb{R}^2$, one can construct an explicit planar polynomial vector field
that realizes $\Gamma$, up to homeomorphism, as the set of its limit cycles
with prescribed periods, multiplicities and stabilities. The only obstruction
given on this data is the obvious compatibility relation between the
stabilities and the parity of the multiplicities. The constructed vector fields
are Darboux integrable and admit a polynomial inverse integrating factor.

13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys