Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two closed geodesics on compact bumpy Finsler manifolds   In this paper, we prove there are at least two closed geodesics on any
compact bumpy Finsler $n$-manifold with $n\ge 2$. Thus generically there are at
least two closed geodesics on compact Finsler manifolds. Furthermore, there are
at least two closed geodesics on any compact Finsler $2$-manifold, and this
lower bound is achieved by the Katok 2-sphere, cf. \cite{Kat}.

13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc