Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Essential hyperbolicity and homoclinic bifurcations: a dichotomy
  phenomenon/mechanism for diffeomorphisms
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys