On the Iteration of Analytic Functions in a Halfplane, I
On the Iteration of Analytic Functions in a Halfplane, I
复制标题
关于半平面中解析函数的迭代，我
DOI：
10.1112/jlms/s2-19.3.439
复制
发表时间：
1979
影响因子：
1.2
通讯作者：
C. Pommerenke
中科院分区：
文献类型：
--
作者：
C. Pommerenke
设i在平面圆盘Q中是解析的，假设i(O)cQ，则迭代数/n(Z)收敛到点GB eQ，除非i是Q到其自身的保角映射。Ce Q案是众所周知的[5；第135页]。在这种情况下，选择Q={\z；1}和C=0比较方便。然后是fn(？)(1-1)(如果/‘(0)=0，则适当修改)，并且Koenigs函数g满足
Let/be analytic in the plane disc Q and suppose that/(O) c Q. Then the iterates/n (z) converge to a point£ e Q, unless/is a conformal mapping of Q onto itself. The case C e Q is well known [5; p. 135]. In this case it is convenient to choose Q={\z\< 1} and C= 0. Then fn (?) lfW-> g®(»->«)(1-1)(with suitable modifications if/'(0)= 0), and the Koenigs function g satisfies the