Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noncommutative Kepler Dynamics: symmetry groups and bi-Hamiltonian
  structures   Integrals of motion are constructed from noncommutative (NC) Kepler dynamics,
generating $SO(3),$ $SO(4),$ and $SO(1,3)$ dynamical symmetry groups. The
Hamiltonian vector field is derived in action-angle coordinates, and the
existence of a hierarchy of bi-Hamiltonian structures is highlighted. Then, a
family of Nijenhuis recursion operators is computed and discussed.

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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys