南方科技大学知识苑(SUSTech KC): Applying the symmetry groups to study the n body problem

题名	Applying the symmetry groups to study the n body problem
作者	Xia，Zhihong 1; Zhou，Tingjie2
通讯作者	Xia，Zhihong
发表日期	2022-02-15
DOI	10.1016/j.jde.2021.11.016
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS 影响因子和分区
ISSN	0022-0396
EISSN	1090-2732
卷号	310页码:302-326
摘要	We introduce an algebraic method to study local stability in the Newtonian n-body problem when certain symmetries are present. We use representation theory of groups to simplify the calculations of certain eigenvalue problems. The method should be applicable in many cases, we give two main examples here: the square central configurations with four equal masses, and the equilateral triangular configurations with three equal masses plus an additional mass of arbitrary size at the center. Using representation theory of finite groups, we explicitly found the eigenvalues of certain 8×8 Hessians in these examples, with only some simple calculations of traces. We also studied the local stability properties of corresponding relative equilibria in the four-body problems.
关键词	Eigenvalues Representation theory Symmetry The Newtonian n-body problem
相关链接	[Scopus记录]
语种	英语
学校署名	其他
ESI学科分类	MATHEMATICS
Scopus记录号	2-s2.0-85119497325
来源库	Scopus
引用统计	被引频次[WOS]：0
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/256905
专题	理学院_数学系
作者单位	1.Department of Mathematics,Northwestern University,Evanston,60208,United States 2.Department of Mathematics,Southern University of Science and Technology,Shenzhen,China
推荐引用方式 GB/T 7714	Xia，Zhihong,Zhou，Tingjie. Applying the symmetry groups to study the n body problem[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2022,310:302-326.
APA	Xia，Zhihong,&Zhou，Tingjie.(2022).Applying the symmetry groups to study the n body problem.JOURNAL OF DIFFERENTIAL EQUATIONS,310,302-326.
MLA	Xia，Zhihong,et al."Applying the symmetry groups to study the n body problem".JOURNAL OF DIFFERENTIAL EQUATIONS 310(2022):302-326.