Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the multiplicity of closed geodesics on Finsler spheres with
  irrationally elliptic closed geodesics   If all prime closed geodesics on $(S^n,F)$ with an irreversible Finsler
metric $F$ are irrationally elliptic, there exist either exactly
$2\left[\frac{n+1}{2}\right]$ or infinitely many distinct closed geodesics. As
an application, we show the existence of three distinct closed geodesics on
bumpy Finsler $(S^3,F)$ if any prime closed geodesic has non-zero Morse index.

6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: math-ph
9
The categories of this paper are: nlin