Periodic Solutions of the Planar N-Center Problem with topological constraints
Periodic Solutions of the Planar N-Center Problem with topological constraints
复制标题
具有拓扑约束的平面N中心问题的周期解
DOI：
10.3934/dcds.2016023
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Guowei Yu
中科院分区：
文献类型：
--
作者：
Guowei Yu
在平面$N$-中心问题中，对于满足一定温和条件的配置空间的非平凡自由同伦类，我们证明了对于任意正的$T，至少存在一个无碰撞的$T-周期解。我们用直接变分的方法证明了在一定的拓扑约束下极小值是无碰撞的。
In the planar $N$-center problem, for a non-trivial free homotopy class of the configuration space satisfying certain mild condition, we show that there is at least one collision free $T$-periodic solution for any positive $T.$ We use the direct method of calculus of variations and the main difficulty is to show that minimizers under certain topological constraints are free of collision.