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

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Abstract

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.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, People’s Republic of China

    Zhiqiang Wang

  2. Department of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, People’s Republic of China

    Shiqing Zhang

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  1. Zhiqiang Wang
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  2. Shiqing Zhang
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Correspondence to Zhiqiang Wang.

Additional information

Communicated by P. Rabinowitz

Dedicated to Professor Kung-Ching Chang for his 80th birthday.

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Wang, Z., Zhang, S. New Periodic Solutions for Newtonian n-Body Problems with Dihedral Group Symmetry and Topological Constraints. Arch Rational Mech Anal 219, 1185–1206 (2016). https://doi.org/10.1007/s00205-015-0919-1

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