一类复动力系统的不动点(英文)

讨论了单位圆盘上的一类积分算子诱导的复动力系统.设f（z）是在单位圆盘（D={︱z︱≤1}）上满足f（0）=0的解析函数,定义复Volterra型算子为（If）（z）=∫0zf（t）dt.研究迭代算子（Jf）（z）=（If）（z）/‖If‖∞的性质,得到对任意n,使得Jnf（z）在边界D上一点z0存在唯一不动点的充分必要条件.

Fixed Point of a Complex Dynamic System

In this paper it is discussed for a complex dynamic system defined by the iteration of the some kinds of integral operators on the unit disk.Assuming that f(z) is an analytic function satisfying f(0) = 0 on the unit disk(D = { |z|≤1}),the Volterra operator is defined by(If)(z) = ∫ z 0 f(t) dt.We study the iteration of the operator(Jf)(z) =(If)(z)‖If‖∞ and obtain some necessary and sufficient conditions that J n f(z) have a common fixed point z 0 on the boundaryD for arbitrary n.