牛顿N体问题里的对称中心构型：存在和分类

The Newtonian N-body problem is a rich source of many mathematical theories, it mainly studies the motion law of N particles affected by their gravitational interactions. General N-body problem is a very complex theoretical problem, and the central configurations plays an important role in the N-body problem, indeed a central role according to Saari. Central configurations satisfy a system of nonlinear algebraic equations, it is very difficult to solve the equations. Hence the researchers firstly study some special central configurations in order to pave the way for understanding more general central configurations. Usually in order to simplify the problem, the researchers reduce the numbers of unknown variables of the central configurations problem by employing some constraints (especially, symmetrical constraint). We will study the symmetrical central configurations by using analytical, algebraic, geometric and topological methods, on the one hand, to find new central configurations, on the other hand, to classify the symmetrical central configurations, so that helping us better understand the central configurations and N-body problem.

牛顿N体问题是许多数学理论的源泉, 它主要研究N个质点在万有引力作用下的运动规律。一般N体问题是一个十分复杂的理论问题，而中心构型在N体问题中具有重要地位，甚至，按照Saari的说法，中心构型具有“中心”地位。中心构型满足一组非线性代数方程，一般很难直接求解。于是人们就先研究一些特殊的中心构型，为进一步理解中心构型做铺垫。通常，人们通过添加约束，尤其是对称约束，来减少问题的参量个数以达到降低困难的目的。本项目将利用分析、代数、几何和拓扑等方法研究对称中心构型，一方面寻找新的中心构型，另一方面尽可能的将对称中心构型分类，以助于更好地理解中心构型和N体问题。