数学科学系

Department of Mathematical Sciences

Keplerian action functional, convex optimization, and n-body problems with only boundary and topological constraints

 

报告题目Keplerian action functional, convex optimization, and n-body problems with only boundary and topological constraints.

 

报告人 Kuo-Chang Chen 陈国璋(台湾清华大学数学系)

 

时间201395(星期四)16:00-17:00

 

地点:理科楼数学系A404

 

摘要: Variational methods have been applied to construct various types of solutions for the n-body problem, under various types of symmetry constraints. However, there were not much success with similar approaches for n-body problems without symmetry and equal-mass constraints, especially when n>3. In this talk we will introduce an apparatus to construct periodic solutions for the n-body problem with only boundary and topological constraints. This approach is a combination of variational arguments in our works on retrograde orbits for the three-body problem and certain constraint convex optimization problems. Our method has no restriction on equal masses. We will illustrate this approach by constructing relative periodic solutions for the planar four-body problems within several topological classes.

 

报告人简介:陈国璋,台湾清华大学教授,2001年在University of Minnesota (Minneapolis) 获得博士学位。曾任台湾理论科学中心“Shiing-Shen Chern Fellow“、曾获得数学会青年数学家奖”、  “国科会”杰出研究奖、   “国科会”吴大猷纪念奖 

       陈国璋教授的研究主要在动态系统、天体力学及变分法。他利用微分方程的方法在多体问题上获得重要突破,研究成果发表于Annals of Mathematics, Communications in Mathematical Physics, American Journal of Mathematics 等国际顶尖期刊。他考虑自由边界多体问题,证明了最小作用力的解处处光滑,并藉此得到另一些周期解与拟周期解。此外,他将变分方法巧妙运用在特定拓朴与对称型式的函数空间,在三体问题证明了大部分质量选取之下逆行解的存在性,克服了变分方法在多体问题应用上的一项关键瓶颈,即等质量的限制。他的研究成果还涵盖了双星系统许多奇异行星轨道的存在性,提供许多天体运行数值模拟结果的理论基础,是古典三体问题研究的显着突破。此成果2008年发表于顶尖期刊Annals of Mathematics。他并引进变分方法至限制多体问题,获得研究限制多体问题的学者肯定与应用。

 

联系人:邹文明