Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615840 | Journal of Mathematical Analysis and Applications | 2014 | 17 Pages |
Abstract
We study the family of renormalization transformations of the generalized d -dimensional diamond hierarchical Potts model in statistical mechanic and prove that their Julia sets and non-escaping loci are always connected, where d⩾2d⩾2. In particular, we prove that their Julia sets can never be a Sierpiński carpet if the parameter is real. We show that the Julia set is a quasicircle if and only if the parameter lies in the unbounded capture domain of these models. Moreover, the asymptotic formula of the Hausdorff dimension of the Julia set is calculated as the parameter tends to infinity.
Keywords
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Fei Yang, Jinsong Zeng,