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A generalized version of Branner-Hubbard conjecture for rational functions

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Abstract

In 1992, Branner and Hubbard raised a conjecture that the Julia set of a polynomial is a Cantor set if and only if each critical component of its filled-in Julia set is not periodic. This conjecture was solved recently. In this paper, we generalize this result to a class of rational functions.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P. R. China

    Yu Zhai

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  1. Yu Zhai
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Correspondence to Yu Zhai.

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Zhai, Y. A generalized version of Branner-Hubbard conjecture for rational functions. Acta. Math. Sin.-English Ser. 26, 2199–2208 (2010). https://doi.org/10.1007/s10114-010-7632-7

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  • DOI: https://doi.org/10.1007/s10114-010-7632-7

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