Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized point vortex dynamics on $CP ^2$   This is the second of two companion papers. We describe a generalization of
the point vortex system on surfaces to a Hamiltonian dynamical system
consisting of two or three points on complex projective space CP^2 interacting
via a Hamiltonian function depending only on the distance between the points.
The system has symmetry group SU(3). The first paper describes all possible
momentum values for such systems, and here we apply methods of symplectic
reduction and geometric mechanics to analyze the possible relative equilibria
of such interacting generalized vortices.
  The different types of polytope depend on the values of the `vortex
strengths', which are manifested as coefficients of the symplectic forms on the
copies of CP^2. We show that the reduced space for this Hamiltonian action for
3 vortices is generically a 2-sphere, and proceed to describe the reduced
dynamics under simple hypotheses on the type of Hamiltonian interaction. The
other non-trivial reduced spaces are topological spheres with isolated singular
points. For 2 generalized vortices, the reduced spaces are just points, and the
motion is governed by a collective Hamiltonian, whereas for 3 the reduced
spaces are of dimension at most 2. In both cases the system will be completely
integrable in the non-abelian sense.

10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin