ON THE DISTRIBUTION OF JULIA SETS OF HOLOMORPHIC MAPS  

作　　者：Chunlei CAO Yuefei WANG 曹春雷;王跃飞(School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,China;College of Mathematics and Statistics,Shenzhen University,Shenzhen 518060,China;Academy of Mathemtics and Systems Sciences,Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,China [2]College of Mathematics and Statistics,Shenzhen University,Shenzhen 518060,China [3]Academy of Mathemtics and Systems Sciences,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Acta Mathematica Scientia》2020年第4期903-909,共7页数学物理学报（B辑英文版）

基　　金：NSF of China(11688101).

摘　　要：In 1965 Baker first considered the distribution of Julia sets of transcendental entire maps and proved that the Julia set of an entire map cannot be contained in any finite set of straight lines.In this paper we shall consider the distribution problem of Julia sets of meromorphic maps.We shall show that the Julia set of a transcendental meromorphic map with at most finitely many poles cannot be contained in any finite set of straight lines.Meanwhile,examples show that the Julia sets of meromorphic maps with infinitely many poles may indeed be contained in straight lines.Moreover,we shall show that the Julia set of a transcendental analytic self-map of C*can neither contain a free Jordan arc nor be contained in any finite set of straight lines.

关 键 词：Fatou set Julia set transcendental analytic map free Jordan arc 

分 类 号：O174.52[理学—数学]