双曲平面上的点涡
Point vortices on the hyperbolic plane
摘要：
研究了双曲面上点涡动力系统的一些性质。该系统具有非紧对称性SL（2，R）和余伴随等变动量映射J，找到了系统的相对平衡条件，并描述了动量值不为零时系统相对平衡的轨迹.我们还提供了相对平衡的分类和稳定性准则的一些情况下，重点是N=2，3。与球面上的系统相反，我们发现了具有非紧动量稳定子群的相对平衡点，并用来说明相对平衡点的不同稳定类型。
英文摘要：
We investigate some properties of the dynamical system of point vortices on the hyperboloid. This system has noncompact symmetry SL(2, R) and a coadjoint equivariant momentum map J. The relative equilibrium conditions are found and the trajectories of relative equilibria with non-zero momentum value are described. We also provide the classification of relative equilibria and the stability criteria for a number of cases, focusing on N=2, 3. Contrary to the system on the sphere, relative equilibria with non-compact momentum isotropy subgroup are found, and are used to illustrate the different stability types of relative equilibria.
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