Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classical and quantum higher order superintegrable systems from
  coalgebra symmetry   The N-dimensional generalization of Bertrand spaces as families of Maximally
superintegrable systems on spaces with nonconstant curvature is analyzed.
Considering the classification of two dimensional radial systems admitting 3
constants of the motion at most quadratic in the momenta, we will be able to
generate a new class of spherically symmetric M.S. systems by using a technique
based on coalgebra. The 3-dimensional realization of these systems provides the
entire classification of classical spherically symmetric M.S. systems admitting
periodic trajectories. We show that in dimension N > 2 these systems (classical
and quantum) admit, in general, higher order constants of motion and turn out
to be exactly solvable. Furthermore it is possible to obtain non radial M.S.
systems by introducing projection of the original radial system to a suitable
lower dimensional space.

11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio