New Periodic Solutions for Newtonian n-Body Problems with Dihedral Group Symmetry and Topological Constraints

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• 作者：Zhiqiang Wang ; Shiqing Zhang
• 刊名：Archive for Rational Mechanics and Analysis
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：219
• 期：3
• 页码：1185-1206
• 全文大小：689 KB
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• 作者单位：Zhiqiang Wang (1)
  Shiqing Zhang (2)
  
  1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, People’s Republic of China
  2. Department of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, People’s Republic of China
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Electromagnetism, Optics and Lasers
  Mathematical and Computational Physics
  Complexity
  Fluids
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0673

文摘

In this paper, we prove the existence of a family of new non-collision periodic solutions for the classical Newtonian n-body problems. In our assumption, the \({n=2l \geqq 4}\) particles are invariant under the dihedral rotation group D _l in \({\mathbb{R}^3}\) such that, at each instant, the n particles form two twisted l-regular polygons. Our approach is the variational minimizing method and we show that the minimizers are collision-free by level estimates and local deformations. Communicated by P. RabinowitzDedicated to Professor Kung-Ching Chang for his 80th birthday.