The existence of noncollision singularities in Newtonian systems. (English) Zbl 0764.70006

Xia, Zhihong

Ann. Math. (2) 135, No. 3, 411-468 (1992).

As an answer to a long-standing problem in celestial mechanics, the contribution of this paper is to prove the existence of noncollision singularities in the 5-body problem. The author studied the isosceles 3- body problem as the first step, then considered a special 5-body problem and constructed unbounded solutions in finite time, in which there is no binary collision involved.

Reviewer: Liu Yanzhu (Shanghai)

MSC:

70F10	\(n\)-body problems
70F35	Collision of rigid or pseudo-rigid bodies
70F15	Celestial mechanics

Keywords:

5-body problem; isosceles 3-body problem; unbounded solutions; finite time