Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Results On The Jacobian Conjecture And Polynomial Automorphisms   In this paper, we will first show that, the homogeneous polynomials which
satisfy the Jacobian condition are injective on the lines that pass through the
origin. Secondly, we will show that $F$ and $G'$ are paired, where $F$ is a
Druzkowski map and $G'$ is a cubic homogeneous polynomial which related to $F$.
Finally, we will find a more exactly bound for the degree of $F^{-1}$, where
$F$ is a invertible map.

37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat