Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonautonomous gradient-like ODEs on the circle: classification,
  structural stability and autonomization   We study a class of scalar differential equations on the circle $S^1$. This
class is characterized mainly by the property that any solution of such an
equation possesses exponential dichotomy both on the semi-axes $\R_+$ and
$\R_+$. Also we impose some other assumptions on the structure of the foliation
into integral curves for such the equation. Differential equations of this
class are called gradient-like ones. As a result, we describe the global
behavior of the foliation, introduce a complete invariant of uniform
equivalency, give standard models for the equations of the distinguished class.
The case of almost periodic gradient-like equations is also studied, their
classification is presented.

8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph