论文标题
Riemann Sphere上的N-涡流问题
The N-vortex Problem on a Riemann Sphere
论文作者
论文摘要
本文调查了Riemann Sphere上的$ n $ - 涡度问题的动态行为$ \mathbfγ$ $ \ mathbb {s}^2 $配备了任意度量$ g $。从Riemannian几何形状和符号几何形状的角度来看，我们研究了不变的轨道，并证明对涡度$ \mathbfγ$的某些约束，$ n $涡度问题具有有限的许多固定点，并且无限地适合通用$ g $。此外，我们验证了涡旋偶极子的超曲面上的接触结构，并排除了不正当的对称轨道的存在。
This article investigates the dynamical behaviours of the $n$-vortex problem with vorticity $\mathbfΓ$ 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 $\mathbfΓ$, 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.
