Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Real Analytic Vector Fields with First Integral and Separatrices   We prove that a germ of analytic vector field at $(\mathbb{R}^3,0)$ that
possesses a non-constant analytic first integral has a real formal separatrix.
We provide an example which shows that such a vector field does not necessarily
have a real analytic separatrix.

19
The categories of this paper are: eess
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat