On the dynamics of a family of generated renormalization transformations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:413

Article

Yang, Fei¹  Zeng, Jinsong² 

[1] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

关键词: Julia sets;    Renormalization transformations;    Hausdorff dimension;   

DOI  :  10.1016/j.jmaa.2013.11.068

来源: Elsevier

【 摘 要 】

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 >= 2. In particular, we prove that their Julia sets can never be a Sierpinski 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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free