Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shadowing, expansiveness and stability of divergence-free vector fields   Let X be a divergence-free vector field defined on a closed, connected
Riemannian manifold. In this paper, we show the equivalence between the
following conditions:
  1. X is in the C1-interior of the set of expansive divergence-free vector
fields.
  2. X is in the C1-interior of the set of divergence-free vector fields which
satisfy the shadowing property.
  3. X is in the C1-interior of the set of divergence-free vector fields which
satisfy the Lipschitz shadowing property.
  4. X has no singularities and X is Anosov.

7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci