Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The N-vortex Problem on a Riemann Sphere   This article investigates the dynamical behaviours of the $n$-vortex problem
with vorticity $\mathbf{\Gamma}$ on a Riemann sphere $\mathbb{S}^2$ equipped
with an arbitrary metric $g$. From perspectives of Riemannian geometry and
symplectic geometry, we study the invariant orbits and prove that with some
constraints on vorticity $\mathbf{\Gamma}$, the $n$-vortex problem possesses
finitely many fixed points and infinitely many periodic orbits for generic $g$.
Moreover, we verify the contact structure on hyper-surfaces of the vortex
dipole, and exclude the existence of perverse symmetric orbits.

15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph