具有牛顿势的圆形限制性四体问题的周期解
Periodic Solutions for Circular Restricted 4-body Problems with Newtonian Potentials
摘要：
本文研究了以下平面限制性4-体问题具有Newton势的非碰撞周期解的存在性：假设Lagrange位形中给定的正质量$m_{1},m_{2},m_{3}$绕质心作圆周运动，充分小的质量绕某物体运动.利用变分极小化方法，证明了反T/2对称环空间上拉格朗日作用的极小元的存在性。此外，我们还证明了极小解是具有固定翼数的非碰撞周期解。
英文摘要：
We study the existence of non-collision periodic solutions with Newtonian potentials for the following planar restricted 4-body problems: Assume that the given positive masses $m_{1},m_{2},m_{3}$ in a Lagrange configuration move in circular obits around their center of masses, the sufficiently small mass moves around some body. Using variational minimizing methods, we prove the existence of minimizers for the Lagrangian action on anti-T/2 symmetric loop spaces. Moreover, we prove the minimizers are non-collision periodic solutions with some fixed wingding numbers.
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