對稱共圓的五體中心構形

Symmetric co-circular five-body central configurations

張格銘(Chang, Ke Ming)

指導教授 ： 陳國璋

國立清華大學/理學院/數學系/碩士(2016年)

摘要

這篇論文中我們探討的是 Chenciner, A. 所提出的一個問題中的某個情況，Chenciner, A.提出的問題是：「共圓而且質心在其外接圓圓心的中型構形是否一定是正多邊形？」，這個問題在三體的情況是對的，不難證明；在四體的情況，由 Hampton, M. 在2003年給了肯定的答案；而我們討論的是五體且對稱的情況，並且證明「對稱、共圓且質心在其外接圓圓心的五體中心構形一定是正五邊形。」

關鍵字

中心構形

並列摘要

In this paper, we study co-circular five-body central configurations with their center of mass at the center of the circumscribed circle. We shall show that in the symmetric case, the only central configuration satisfying these conditions is the regular pentagon with equal masses.

並列關鍵字

central configuration

參考文獻

Albouy, A., Kaloshin, V., Finiteness of central configurations for five bodies in the plane., Ann. Math. 176, 535 - 588 (2012)

Chenciner, A., Are there perverse choreographs?, to appear in the proceedings of the 2001 HAMSYS Conference in Guanajuato, Mexico.

Chen, K.-C., Hsiao, J.-S., Strictly convex central configurations of the planar five-body problem., Trans. Amer. Math.

Hampton, M., Co-circular central configurations in the four-body problem., Equadiff 2003. Proceedings of the International Conference on Differential Equations, pp.

Hampton, M., Moeckel, R. Finiteness of relative equilibria of the four-body problem., Invent. Math. 163, 289 - 312 (2006)