不可可定向曲面II上点涡的Hamilton方法：克莱因瓶
A Hamiltonian approach for point vortices on non-orientable surfaces II: the Klein bottle
摘要：
这是致力于研究不可可定向曲面上涡流运动的两篇姊妹论文中的第二篇。第一份文件对主要是关注建立哈密顿方法系统的点涡对非可定向流形和调查的限制内在（限于非可定向流形）的办法。此外，莫比乌斯带上的点涡运动进行了仔细检查。本文通过建立显式的哈密顿量、运动方程和描述相对平衡等方法，研究了克莱因瓶上单点和两点涡的动力学。
英文摘要：
This is the second of two companion papers dedicated to the investigation of vortex motion on non-orientable surfaces. The first paper of the pair is predominantly concerned with establishing the Hamiltonian approach to systems of point vortices on non-orientable manifolds and investigating the limits of the intrinsic (restricted to the non-orientable manifold) approach. In addition, point vortex motion on the Mobius band is closely examined. In this paper, we investigate dynamics of one and two point vortices on the Klein bottle through establishing explicit forms of the Hamiltonian, equations of motion on the charts, describing relative equilibria, etc.
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