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Cubic Rational Maps with Escaping Critical Points, Part I: Julia Set Dichotomy in the Case of an Attracting Fixed Point

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Abstract

The Julia set of any quadratic rational map is either connected or a Cantor set. In this paper, we extend this dichotomy to any cubic rational map with all critical points escaping to an attracting fixed point.

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Acknowledgements

Both authors are grateful to Professors Weiyuan Qiu and Mistu Shishikura for several useful comments and suggestions. They also wish to thank the referees for their comments and corrections of typos.

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Authors and Affiliations

  1. Department of Mathematics, Brooklyn College of CUNY, Brooklyn, NY, 11210, USA

    Jun Hu

  2. Ph.D. Program in Mathematics, Graduate Center of CUNY, 365 Fifth Avenue, New York, NY, 10016, USA

    Jun Hu & Arkady Etkin

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  1. Jun Hu
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  2. Arkady Etkin
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Correspondence to Jun Hu.

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Partially supported

The work of Jun Hu was partially supported by Research Foundation of The City University of New York under PSC-CUNY Award \(\#\) 62084-00 50.

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Hu, J., Etkin, A. Cubic Rational Maps with Escaping Critical Points, Part I: Julia Set Dichotomy in the Case of an Attracting Fixed Point. Qual. Theory Dyn. Syst. 21, 70 (2022). https://doi.org/10.1007/s12346-022-00593-y

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  • DOI: https://doi.org/10.1007/s12346-022-00593-y

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