Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase topology of one system with separated variables and singularities
  of the symplectic structure   We consider an example of a system with two degrees of freedom admitting
separation of variables but having a subset of codimension 1 on which the
2-form defining the symplectic structure degenerates. We show how to use
separation of variables to calculate the exact topological invariant of
non-degenerate singularities and singularities appearing due to the symplectic
structure degeneration. New types of non-orientable 3-atoms are found.

27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess