Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polycycle omega-limit sets of flows on the compact Riemann surfaces and
  Eulerian path   Let $(S,\Phi)$ be a pair of a closed oriented surface and $\Phi$ be a real
analytic flow with finitely many singularities. Let $x$ be a point of $S$ with
the polycycle $\omega$-limit set $\omega(x)$. In this paper we give topological
classification of $\omega(x)$. Our main theorem says that $\omega(x)$ is
diffeomorphic to the boundary of a cactus in the $2$-sphere $S^{2}$. Moreover
$S$ is a connected sum of the above $S^{2}$ and a closed oriented surface along
finitely many embedded circles which are disjoint from $\omega(x)$. This gives
a natural generalization to the higher genus of the main result of \cite{JL}
for the genus $0$ case. Our result is further applicable to a larger class of
surface flows, a compact oriented surface with corner and a $C^{1}$-flow with
finitely many singularities locally diffeomorphic to an analytic flow.

14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph