Hausdorf Dimension of Quadratic Rational Julia Sets  

作　　者：Jia ZHOU Liang Wen LIAO 

机构地区：[1]Department of Mathematics,Nanjing University

出　　处：《Acta Mathematica Sinica,English Series》2014年第2期331-342,共12页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.10871089 and 11271179)

摘　　要：Suppose a quadratic rational map has a Siegel disk and a parabolic fixed point. If the rotation number of the Siegel disk is an irrational of bounded type, then the Julia set of the map is shallow. This implies that its Hausdorff dimension is strictly less than two.Suppose a quadratic rational map has a Siegel disk and a parabolic fixed point. If the rotation number of the Siegel disk is an irrational of bounded type, then the Julia set of the map is shallow. This implies that its Hausdorff dimension is strictly less than two.

关 键 词：SHALLOW Julia sets quadratic rational map Hausdorff dimension 

分 类 号：O144[理学—数学]