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

2015/01/31 by Zhiqiang Wang, Shiqing Zhang · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP

paper · pdf · doi:10.1007/s00205-015-0919-1

arxiv created 2015/03/12 · arxiv updated 2015/09/30

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≥4 particles are invariant under the dihedral rotation group D_l in ℝ³ such that, at each instant, the n particles form two twisted l-regular polygons. Our approach is variational minimizing method and we show that the minimizers are collision-free by level estimates and local deformations.

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