Dynamics of a family of rational maps concerning renormalization transformation

doi:10.1007/s11464-020-0854-9

Front. Math. China

2020, Vol. 15

Issue (4) : 807-833 https://doi.org/10.1007/s11464-020-0854-9

RESEARCH ARTICLE

Dynamics of a family of rational maps concerning renormalization transformation

Yuhan ZHANG¹, Junyang GAO¹(

), Jianyong QIAO², Qinghua WANG¹

¹. School of Science, China University of Mining and Technology, Beijing 100083, China
². School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

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Abstract

Considering a family of rational maps $T n λ$ concerning renormalization transformation, we give a perfect description about the dynamical properties of $T n λ$ and the topological properties of the Fatou components F ( $T n λ$ ). Furthermore, we discuss the continuity of the Hausdorff dimension HD(J ( $T n λ$ )) about real parameter λ.

Keywords Completely invariant domain quasi-circle Hausdorff dimension renormalization transformation

Corresponding Author(s): Junyang GAO

Issue Date: 09 September 2020

Cite this article:

Yuhan ZHANG,Junyang GAO,Jianyong QIAO, et al. Dynamics of a family of rational maps concerning renormalization transformation[J]. Front. Math. China, 2020, 15(4): 807-833.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0854-9
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I4/807

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