非光滑有界凸域上全纯自映射的随机迭代  

Random Iteration of Holomorphic Self-Maps on Non-Smooth Bounded Convex Domain

作　　者：杨利琴 邓方文[2] 

机构地区：[1]武汉海事职业学院,武汉430311 [2]中国科学院武汉物理与数学研究所,武汉430071

出　　处：《数学物理学报（A辑）》2015年第6期1127-1135,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(11271359)资助

摘　　要：该文在经典的Wolff-Denjoy理论的基础上研究C^n中有界严格凸域与有界弱凸域上随机迭代的收敛性问题.给出了有界严格凸域中全纯映射的随机迭代存在内闭一致收敛到边界上的常值映射的子序列的限制条件;而在有界弱凸域中,所给的限制条件强了很多,但全纯映射的随机迭代的收敛性却减弱了.该文所给定理的证明方法可以证明单个解析函数的相应结果的迭代理论.In this paper,we study random iterative convergence problem on bounded strictly convex and bounded weak convex domain in C-n based on the classical Wolff-Denjoy theorem.On bounded strictly convex domain,we prove that there exists a supsequence which converges uniformly to constant map on the boundary under some condition.On bounded weak convex domain,the restrictive condition becomes stronger,but the convergence result becomes weaker.The method in this paper can be used to prove the iterative theorem of single analytic function.

关 键 词：随机迭代 有界凸域 收敛性 全纯映射. 

分 类 号：O1-0[理学—数学]