Connectivity of the Mandelbrot set for the family of renormalization transformations

• 出 处: 中国科学：数学英文版
• 发表日期: 2010年3期
• 关键词: CONNECTIVITY Mandelbrot SET RENORMALIZATION TRANSFORMATIONS connectivityMandelbr
• 基金项目: supported by National Natural Science Foundation of China (Grant Nos.10625107, 10801134, 10831004 and 10871047),Natural Science Foundation of Shanghai, China (Grant No.10ZR1403700)

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