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Topological properties of certain iterated entire maps

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Abstract

In this paper it is shown that for a transcendental entire map with certain properties on the distribution of either its zeros, or points in its periodic and preperiodic Fatou domains, all of its Fatou components are simply connected, the union of its Julia set and \(\{ \infty \}\) is connected and the Julia set is uniformly perfect. Moreover, it is shown that any transcendental entire map that interpolates the 3n+1 problem has only simply connected Fatou components and its Julia set is uniformly perfect.

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Acknowledgements

The authors are grateful to the National Center for Applied Mathematics Shenzhen (NCAMS) for supports.

Funding

The authors are partially supported by the National Natural Science Foundation of China, Grant No. 12231013.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    Chunlei Cao

  2. School of Mathematics, Shenzhen University and Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100080, China

    Yuefei Wang

  3. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Huayu Zhao

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  1. Chunlei Cao
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  2. Yuefei Wang
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  3. Huayu Zhao
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Contributions

CC, YW and HZ wrote the main manuscript text and CC prepared the figure 1. All authors reviewed the manuscript.

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Correspondence to Yuefei Wang.

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The authors are supported by NSFC (grant No. 12231013) and NKRDPC (grant No. 2021YFA1003203).

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Cao, C., Wang, Y. & Zhao, H. Topological properties of certain iterated entire maps. Anal.Math.Phys. 14, 18 (2024). https://doi.org/10.1007/s13324-024-00879-1

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  • DOI: https://doi.org/10.1007/s13324-024-00879-1

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