一类复动力系统的不动点

摘要

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.%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 Voherra operator is defined by （If）（z）=∫0zf（t）dt.We study the iteration of the operator （Jf）（z）=（If）（z）/‖If‖∞ and obtain some necessary and sufficient conditions that Jnf（z） have a common fixed point z0 on the boundary D for arbitrary n.