本文利用等变的Ｌｊｕｓｔｅｒｎｉｋ－Ｓｃｈｎｉｒｅｌｍａｎｎ理论证明了平面上的一类给定能量的Ｎ体型问题至少存在２·（Ｎ—２）·２Ｎ－３个几何上不同的非碰撞周期轨道．

Using the equivariant Ljusternik-Schnirelmann theory, we prove that there are at least 2·(N-2)·N-3 geometrically distinct noncollision orbits with prescribed energy for a class of planar N-body-type problems.