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Connectivity of the Mandelbrot set for the family of renormalization transformations |
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| Authors: | WANG XiaoGuang QIU WeiYuan YIN YongCheng QIAO JianYong & GAO JunYang School of Mathematical Sciences Fudan University Shanghai China Center of Mathematics China University of Mining Technology Beijing |
| Institution: | 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 , Technology,Beijing 100083 |
| Abstract: | 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. |
| Keywords: | connectivity Mandelbrot set renormalization transformations |
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