Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A topological characterization of the omega-limit sets of analytic
  vector fields on open subsets of the sphere   In [15], V. Jimenez and J. Llibre characterized, up to homeomorphism, the
omega limit sets of analytic vector fields on the sphere and the projective
plane. The authors also studied the same problem for open subsets of these
surfaces.
  Unfortunately, an essential lemma in their programme for general surfaces has
a gap. Although the proof of this lemma can be amended in the case of the
sphere, the plane, the projective plane and the projective plane minus one
point (and therefore the characterizations for these surfaces in [8] are
correct), the lemma is not generally true, see [15].
  Consequently, the topological characterization for analytic vector fields on
open subsets of the sphere and the projective plane is still pending. In this
paper, we close this problem in the case of open subsets of the sphere.

13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci