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Dynamics of a family of rational maps concerning renormalization transformation

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Abstract

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

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11571049) and the Special Basic Scientific Research Funds of Central Universities in China.

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Authors and Affiliations

  1. School of Science, China University of Mining and Technology, Beijing, 100083, China

    Yuhan Zhang, Junyang Gao & Qinghua Wang

  2. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Jianyong Qiao

Authors
  1. Yuhan Zhang
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  2. Junyang Gao
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  3. Jianyong Qiao
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  4. Qinghua Wang
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Correspondence to Junyang Gao.

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Zhang, Y., Gao, J., Qiao, J. et al. Dynamics of a family of rational maps concerning renormalization transformation. Front. Math. China 15, 807–833 (2020). https://doi.org/10.1007/s11464-020-0854-9

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  • DOI: https://doi.org/10.1007/s11464-020-0854-9

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