Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant manifolds for piecewise smooth differential systems in
  $\mathbb{R}^{3}$   In this paper some piecewise smooth perturbations of a three-dimensional
differential system are considered. The existence of invariant manifolds filled
by periodic orbits is obtained after suitable small perturbations of the
original differential system. These manifolds emerge from a continuum of
cylinders of $\mathbb{R}^3$ which does exist for the piecewise smooth
differential systems after a rotation of some planar algebraic polynomial
curves. The main tool used in order to obtain the results is the averaging
theory for piecewise smooth differential systems.

22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph