关于N-体问题的几个重要猜想

具有牛顿弱力势的多体问题来源于1687年出版的牛顿的巨著《自然哲学的数学原理》，由于某个质点受到的作用力是其它质点对它的万有引力的合力，而引力的大小与距离的平方成反比，因此多体问题运动方程组是高度非线性的，而且还可能出现奇性。. 牛顿、贝努利时代已经知道二体问题的通解是二次曲线，牛顿曾试图求解三体问题时，他失败了，他认为这是一个使他头痛的问题，从牛顿时代到二十一世纪初的三百多年，许多数学家、天文学家、物理学家都曾研究过多体问题，取得了丰硕的成果。. 多体问题中还有一些重要问题没能完全解决，如平面初值问题的非碰撞奇性，无穷旋转问题与中心构型有限性猜想，Saari 猜想，周期解的分类及稳定性，解的渐近行为的分类等。. 我们尝试寻找分析、代数、几何和拓扑中合适的思想和方法来解决多体问题中的几个长期未解决的猜想。

Many body problems with Newtonian weak force potentials came from Newton's great book "Mathematical Principles of Natural Philosophy" published in 1687. Since the infected force for some mass point is the sum for gravitational forces affected by the other bodies, and the magnituds for gravitational forces are inverse square to their distances, hence the motion equations for many body problems are highly nonlinear, and singularities may appear.. In the time of Isaac Newton and John Bernoulli, they knew the general solutions of two body problems are conic curves, Newton tried to solve three body problems, but he failed, he thought this problem made him headache. During more than 300 years from the time of Isaac Newton to 21th Century, many mathematicians and physicians and astronomers studied the many body problems, and got many important results.. There are some important problems unsolved completely in the many body problems, such as, noncollision singularities for planar initial value problems, infinitely spin problems, the conjecture on finite many central configurations, Saari 's conjecture, the classifications and stabilities for periodic solutions, the classifications for the asymptotic behaviors of solutions .. We try to look for suitable ideas and methods from analysis, algebra, geometry and topology to solve these outstanding conjectures.