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.
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Dedicated to Professor Yang Lo on the Occasion of his 70th Birthday
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Wang, X., Qiu, W., Yin, Y. et al. Connectivity of the Mandelbrot set for the family of renormalization transformations. Sci. China Math. 53, 849–862 (2010). https://doi.org/10.1007/s11425-010-0034-6
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DOI: https://doi.org/10.1007/s11425-010-0034-6