超越整函数半群的游荡域

Wandering Domains of Semigroups of Transcendental Entire Functions

设G是由一族超越整函数生成的半群,其中半群运算是函数的复合.在满足某些假设下,文中得到G在其游荡域内的极限函数要么是∞,要么属于G中某个函数φ的奇异值集合singφ^(-1)的导集.

Let G be a semigroup generated by a family of transcendental entire functions with the semigroup operation being functional composition.Under some conditions,it is shown that any limit function of G in wandering domains is∞or lies in the derived set of singφ^-1 for someφ∈G.