Connectivity of the Mandelbrot set for the family of renormalization transformations  

作　　者：WANG XiaoGuang 1,QIU WeiYuan 1 , YIN YongCheng 1 , QIAO JianYong 2 & GAO JunYang 2 1 School of Mathematical Sciences, Fudan University, Shanghai 200433, China 2 Center of Mathematics, China University of Mining and Technology, Beijing 100083, China 

出　　处：《Science China Mathematics》2010年第3期849-862,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos.10625107, 10801134, 10831004 and 10871047);Natural Science Foundation of Shanghai, China (Grant No.10ZR1403700)

摘　　要：We show that the Mandelbrot set for the family of renormalization transformations of 2-dimensional diamond-like hierachical Potts models in statistical mechanics is connected. We also give an upper bound for the Hausdorff dimension of Julia set when it is a quasi-circle.We show that the Mandelbrot set for the family of renormalization transformations of 2-dimensional diamond-like hierachical Potts models in statistical mechanics is connected. We also give an upper bound for the Hausdorff dimension of Julia set when it is a quasi-circle.

关 键 词：CONNECTIVITY Mandelbrot SET RENORMALIZATION TRANSFORMATIONS 

分 类 号：O174.14[理学—数学]