Hausdorff dimension of quadratic rational Julia sets |
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| Authors: | Jia Zhou Liang Wen Liao |
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| Institution: | 1. Department of Mathematics, Nanjing University, Nanjing, 210093, P. R. China
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| Abstract: | Suppose a quadratic rational map has a Siegel disk and a parabolic fixed point. If the rotation number of the Siegel disk is an irrational of bounded type, then the Julia set of the map is shallow. This implies that its Hausdorff dimension is strictly less than two. |
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| Keywords: | Shallow Julia sets quadratic rational map Hausdorff dimension |
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