拟亚纯映射的奇异方向和迭代

【作者】 吴昭君；

【导师】 孙道椿；

【作者基本信息】 华南师范大学 ， 基础数学， 2005， 硕士

【摘要】 本文运用Ahlfors覆盖曲面的方法研究了平面上的一类广泛的复函数-拟亚纯映射的奇异方向和迭代。首先,证明了平面上拟亚纯映射的Julia方向,Borel方向和最大型Borel方向的存在性和一些判定条件,推广了亚纯函数和亚纯代数体函数的相关结果。然后,定义了平面上的拟多项式,描述了拟多项式在迭代过程中的一些动力性质,得到了一些与多项式动力系统相类似结果。更多还原

【Abstract】 In this paper, by using Ahlfors’s covering surface method, the more general quasimeromorphic mappings are studied, the Julia directions, Borel directions , the largest type Borel directions of quasimeromorphic mappings and the iterations of quasipolynomial mappings are discussed. The following results have been obtained:(1) Two precise theorems of Julia direction are proved.(2)The definition of the largest type Borel directions is introduced,and its existence be proved.The necessary and sufficient condition for judging the largest type Borel direction of K-quasimeromorphic mappings are obtained.(3)The relations between Borel direction and the largest type Borel direction have been discussed, as well as one necesssary and sufficient condition of judging Borel direction of quasimeromorphic mapping is proved.(4) The iteration of quasipolynomial mappings are discussed, some theorems about the escaping set, filling Julia set and Julia set are proved.At the same time, the iterations of two permutable quasipolynomial mappings be discussed.更多还原