Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Goldfish geodesics and Hamiltonian reduction of matrix dynamics   We relate free vector dynamics to the eigenvalue motion of a time-dependent
real-symmetric NxN matrix, and give a geodesic interpretation to Ruijsenaars
Schneider models.

10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas