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arXiv · 2106.07450

Local connectivity of Julia sets of some rational maps with Siegel disks

Shuyi Wang·Fei Yang·Gaofei Zhang·Yanhua Zhang
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Abstract

We prove that a long iteration of rational maps is expanding near boundaries of bounded type Siegel disks. This leads us to extend Petersen's local connectivity result on the Julia sets of quadratic Siegel polynomials to a general case. A new key feature in the proof is that the puzzles are not used.

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Shuyi Wang, Fei Yang, Gaofei Zhang, Yanhua Zhang. 2021-06-14. Local connectivity of Julia sets of some rational maps with Siegel disks. https://arxiv.org/abs/2106.07450

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