Simple Choreographies of the Planar Newtonian N-Body Problem

被引：18
|
作者：
Yu, Guowei [1 ,2 ,3 ]
机构：
[1] Univ Toronto, Dept Math, Toronto, ON, Canada
[2] Univ Paris 09, CEREMADE, Paris, France
[3] Paris Observ, IMCCE, Paris, France
来源：
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2017年 / 225卷 / 02期
关键词：
ACTION-MINIMIZING ORBITS; PERIODIC-SOLUTIONS; 3-BODY PROBLEM; EXISTENCE;
D O I：
10.1007/s00205-017-1116-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the N-body problem, a simple choreography is a periodic solution, where all masses chase each other on a single loop. In this paper we prove that for the planar Newtonian N-body problem with equal masses, N ae 3, there are at least 2 (N-3) + 2([(N-3)/2]) different main simple choreographies. This confirms a conjecture given by Chenciner et al. (Geometry, mechanics, and dynamics. Springer, New York, pp 287-308, 2002). All the simple choreoagraphies we prove belong to the linear chain family.
引用
收藏
页码：901 / 935
页数：35
相关论文
共 50 条
12345