A generalized version of Branner-Hubbard conjecture for rational functions |
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| Authors: | Yu Zhai |
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| Affiliation: | 1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P. R. China
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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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| Keywords: | Julia set filled-in Julia set Branner-Hubbard puzzle KSS nest |
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