Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Birth of limit cycles for a class of continuous and discontinuous
  differential systems in (d+2)-dimension   The orbits of the reversible differential system $\dot{x}=-y$, $\dot{y}=x$,
$\dot{z}=0$, with $x,y \in R$ and $z\in R^d$, are periodic with the exception
of the equilibrium points $(0,0, z)$. We compute the maximum number of limit
cycles which bifurcate from the periodic orbits of the system $\dot{x}=-y$,
$\dot{y}=x$, $\dot{z}=0$, using the averaging theory of first order, when this
system is perturbed, first inside the class of all polynomial differential
systems of degree $n$, and second inside the class of all discontinuous
piecewise polynomial differential systems of degree $n$ with two pieces, one in
$y> 0$ and the other in $y<0$. In the first case this maximum number is
$n^d(n-1)/2$, and in the second is $n^{d+1}$.

10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an