@article{Li2022, 
author = {Tingting Li and Junyang Gao},
title = {The Hausdorff dimension of the Julia sets concerning generated renormalization transformation},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {1},
pages = {939-956},
keywords = {renormlization transformation, Potts model, asymptotic formula, Hausdorff dimension, Julia set},
url = {https://www.sciopen.com/article/10.3934/math.2022056},
doi = {10.3934/math.2022056},
abstract = {Considering a family of rational map              U              m        n        λ             of the renormalization transformation of the generalized diamond hierarchical Potts model, we give the asymptotic formula of the Hausdorff dimension of the Julia sets of              U              m        n        λ             as the parameter    λ tends to infinity, here               U              m        n        λ              =                    [                                                                                                                        (                                              z                        +                        λ                        −                        1                                            )                                                        n                                            +                              (                                  λ                  −                  1                                )                                                                                                        (                                              z                        −                        1                                            )                                                        n                                                                                                                                                (                                              z                        +                        λ                        −                        1                                            )                                                        n                                            −                                                                                          (                                              z                        −                        1                                            )                                                        n                                                                    ]            m        ,where    m  ≥  2,    n  ≥  2 are two natural numbers,    λ  ∈                    C            .}
}