Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the existence of infinitely many closed geodesics on orbifolds of
  revolution   Using the theory of geodesics on surfaces of revolution, we introduce the
period function. We use this as our main tool in showing that any
two-dimensional orbifold of revolution homeomorphic to S^2 must contain an
infinite number of geometrically distinct closed geodesics. Since any such
orbifold of revolution can be regarded as a topological two-sphere with metric
singularities, we will have extended Bangert's theorem on the existence of
infinitely many closed geodesics on any smooth Riemannian two-sphere. In
addition, we give an example of a two-sphere cone-manifold of revolution which
possesses a single closed geodesic, thus showing that Bangert's result does not
hold in the wider class of closed surfaces with cone manifold structures.

4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn