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On the dynamics of a family of generated renormalization transformations.
- Source :
-
Journal of Mathematical Analysis & Applications . May2014, Vol. 413 Issue 1, p361-377. 17p. - Publication Year :
- 2014
-
Abstract
- 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 . In particular, we prove that their Julia sets can never be a SierpiĆski 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. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 413
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 94076718
- Full Text :
- https://doi.org/10.1016/j.jmaa.2013.11.068