Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrable Hamiltonian systems on symmetric spaces: Jacobi, Kepler and
  Moser   This paper defines a class of variational problems on Lie groups that admit
involutive automorphisms. The maximum Principle of optimal control then
identifies the appropriate left invariant Hamiltonians on the Lie algebra of
the group. The corresponding Hamiltonian equations admit a spectral
representation with important applications to the theory of integrable systems.
Particular cases make a link to Moser's work relating the solutions of Kepler's
problem to the geodesics on spaces of constant curvature, Newmann's mechanical
problem on the sphere and related geodesic problem of Jacobi on an ellipsoid.

18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics