Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-symplectic symmetries and bi-Hamiltonian structures of the rational
  Harmonic Oscillator   The existence of bi-Hamiltonian structures for the rational Harmonic
Oscillator (non-central harmonic oscillator with rational ratio of frequencies)
is analyzed by making use of the geometric theory of symmetries. We prove that
these additional structures are a consequence of the existence of dynamical
symmetries of non-symplectic (non-canonical) type. The associated recursion
operators are also obtained.

29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
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The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ