关于平面五涡问题稳态构型有限性的研究
On Finiteness of Stationary Configurations of the Planar Five-vortex Problem
AI总结：
本文研究了平面五涡问题中稳态构型的有限性，证明了平衡与刚性平移构型数量的上界，并指出在涡量同号等条件下稳态构型数量有限。
摘要：
本文考虑了平面五涡问题中稳态构型的有限性问题。平衡和刚性平移构型的数量分别被证明至多为6和24。相对平衡和塌陷构型的数量被证明是有限的，除非5元涡量属于涡量空间中给定的余维数2子簇。特别地，如果涡量同号，则稳态构型的数量是有限的。
英文摘要：
The finiteness problem of stationary configurations for the planar five-vortex problem is considered in this paper. The numbers of equilibria and rigidly translating configurations are shown to be at most 6 and 24 respectively. The numbers of relative equilibria and collapse configurations are shown to be finite, except perhaps if the 5-tuple of vorticities belongs to a given codimension 2 subvariety of the vorticity space. In particular, if the vorticities are of the same sign, the number of stationary configurations is finite.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
