Euler configurations and quasi-polynomial systems
文献类型：期刊论文
| 作者 | Albouy, A.; Fu, Y. |
| 刊名 | REGULAR & CHAOTIC DYNAMICS
 |
| 出版日期 | 2007 |
| 卷号 | 12期号:1页码:39-55 |
| 关键词 | relative equilibria point vortex real solutions |
| ISSN号 | 1560-3547 |
| 英文摘要 | Consider the problem of three point vortices ( also called Helmholtz' vortices) on a plane, with arbitrarily given vorticities. The interaction between vortices is proportional to 1/r, where r is the distance between two vortices. The problem has 2 equilateral and at most 3 collinear normalized relative equilibria. This 3 is the optimal upper bound. Our main result is that the above standard statements remain unchanged if we consider an interaction proportional to r(b), for any b < 0. For 0 < b < 1, the optimal upper bound becomes 5. For positive vorticities and any b < 1, there are exactly 3 collinear normalized relative equilibria. The case b = -2 of this last statement is the wellknown theorem due to Euler: in the Newtonian 3-body problem, for any choice of the 3 masses, there are 3 Euler configurations ( also known as the 3 Euler points). These small upper bounds strengthen the belief of Kushnirenko and Khovanskii [ 18]: real varieties defined by simple systems should have a simple topology. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework. |
| WOS标题词 | Science & Technology ; Physical Sciences ; Technology |
| 学科主题 | Astronomy & Astrophysics |
| 类目[WOS] | Mathematics, Applied ; Mechanics ; Physics, Mathematical |
| 研究领域[WOS] | Mathematics ; Mechanics ; Physics |
| 关键词[WOS] | RELATIVE EQUILIBRIA ; BIFURCATIONS ; FINITENESS ; DISTANCE ; ORBITS ; BODY |
| 收录类别 | SCI |
| 语种 | 英语 |
| WOS记录号 | WOS:000250845900004 |
| 公开日期 | 2012-02-05 |
| 源URL | [http://159.226.72.40/handle/332002/2354]  |
| 专题 | 紫金山天文台_历算和天文参考系研究团组 |
| 作者单位 | 1.IMCCE, F-75014 Paris, France 2.Purple Mt Observ, Nanjing 210008, Peoples R China |
| 推荐引用方式 GB/T 7714 | Albouy, A.,Fu, Y.. Euler configurations and quasi-polynomial systems[J]. REGULAR & CHAOTIC DYNAMICS,2007,12(1):39-55. |
| APA | Albouy, A.,&Fu, Y..(2007).Euler configurations and quasi-polynomial systems.REGULAR & CHAOTIC DYNAMICS,12(1),39-55. |
| MLA | Albouy, A.,et al."Euler configurations and quasi-polynomial systems".REGULAR & CHAOTIC DYNAMICS 12.1(2007):39-55. |
入库方式： OAI收割
来源：紫金山天文台
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