Connectivity of the Mandelbrot set for the family of renormalization transformations

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.

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Bibliographic Details
Published in:Science China. Mathematics 2010-03, Vol.53 (3), p.849-862
Main Authors: Wang, XiaoGuang, Qiu, WeiYuan, Yin, YongCheng, Qiao, JianYong, Gao, JunYang
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-010-0034-6