Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Birth of isolated nested cylinders and limit cycles in 3D piecewise
  smooth vector fields with symmetry   Our start point is a 3D piecewise smooth vector field defined in two zones
and presenting a shared fold curve for the two smooth vector fields considered.
Moreover, these smooth vector fields are symmetric relative to the fold curve,
giving raise to a continuum of nested topological cylinders such that each
orthogonal section of these cylinders is filled by centers. First we prove that
the normal form considered represents a whole class of piecewise smooth vector
fields. After we perturb the initial model in order to obtain exactly
$\mathcal{L}$ invariant planes containing centers. A second perturbation of the
initial model also is considered in order to obtain exactly $k$ isolated
cylinders filled by periodic orbits. Finally, joining the two previous
bifurcations we are able to exhibit a model, preserving the symmetry relative
to the fold curve, and having exactly $k.\mathcal{L}$ limit cycles.

3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph