n维Mobius变换中的两个Beardon定理

The Generalizations of Two Beardon's Theorems

将Ａ．Ｆ．Ｂｅａｒｄｏｎ在平面Ｍｂｉｕｓ群中的两个定理推广到了ｎ维空间，得到了；（１）若有一公共不动点０或∞，则ｔｒ［ｆ，ｇ］＝２的充要条件是ａα＝αａ．（２）若ｆ是严格抛物元素，＜ｆ，ｇ＞是非初等离散群，则及当ｇ也是严格抛物元素时有，其中ｘ∈Ｈｎ＋１．

In this paper we have obtained the generalizations of two Beardon's theorems. We have proved the following main results: (1) if f= and in SL(2, Γn) have a common fixed point 0 or ∞, then tr[f, g] = 2 if and only if aα=αa, (2) If f is uniformly parabolic, (f, g) is a non-elementary discrete group, then and if g is also uniformly parabolic, thensinh sinh all x in Hn+1