Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Lower bounds on the number of closed trajectories of generalized
  billiards
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc