Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the number of limit cycles which appear by perturbation of
  Hamiltonian two-saddle cycles of planar vector fields   We find an upper bound to the maximal number of limit cycles, which bifurcate
from a hamiltonian two-saddle loop of an analytic vector field, under an
analytic deformation.

24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: eess
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph