Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A global geometric decomposition of vector fields and applications to
  topological conjugacy   We give a global geometric decomposition of continuously differentiable
vector fields on $\mathbb{R}^n$. More precisely, given a vector field of class
$\mathcal{C}^{1}$ on $\mathbb{R}^{n}$, and a geometric structure on
$\mathbb{R}^n$, we provide a unique global decomposition of the vector field as
the sum of a left (right) gradient--like vector field (naturally associated to
the geometric structure) with potential function vanishing at the origin, and a
vector field which is left (right) orthogonal to the identity, with respect to
the geometric structure. As application, we provide a criterion to decide
topological conjugacy of complete vector fields of class $\mathcal{C}^1$ on
$\mathbb{R}^{n}$ based on topological conjugacy of the corresponding parts
given by the associated geometric decompositions.

13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys