Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homoclinic classes for generic C^1 vector fields   We prove that homoclinic classes for a residual set of C^1 vector fields X on
closed n-manifolds are maximal transitive and depend continuously on periodic
orbit data. In addition, X does not exhibit cycles formed by homoclinic
classes. We also prove that a homoclinic class of X is isolated if and only if
it is Omega-isolated, and that it is the intersection of its stable set and its
unstable set. All these properties are well known for structurally stable Axiom
A vector fields.

5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
9
The categories of this paper are: nlin