New Periodic Solutions for Newtonian n-Body Problems with Dihedral Group Symmetry and Topological Constraints
New Periodic Solutions for Newtonian n-Body Problems with Dihedral Group Symmetry and Topological Constraints
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DOI：
10.1007/s00205-015-0919-1
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发表时间：
2015-01
影响因子：
2.5
通讯作者：
Zhiqiang Wang;Shiqing Zhang
中科院分区：
文献类型：
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作者：
Zhiqiang Wang;Shiqing Zhang
本文证明了经典牛顿体问题一族新的非碰撞周期解的存在性。在我们的假设中，粒子在二面角旋转群Dlin下是不变的，使得在每个时刻，粒子形成两个扭曲的l-正多边形。我们的方法是变分最小化方法，我们表明，最小的水平估计和局部变形是无碰撞的。
In this paper, we prove the existence of a family of new non-collision periodic solutions for the classical Newtoniann-body problems. In our assumption, theparticles are invariant under the dihedral rotation groupDlinsuch that, at each instant, thenparticles form two twistedl-regular polygons. Our approach is the variational minimizing method and we show that the minimizers are collision-free by level estimates and local deformations.