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arXiv · 2010.14003

Local Connectivity of Polynomial Julia sets at Bounded Type Siegel Boundaries

Jonguk Yang
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Abstract

Consider a polynomial $f$ of degree $d \geq 2$ that has a Siegel disk $\Delta_f$ with a rotation number of bounded type. We prove that there does not exist a hedgehog containing $\Delta_f$. Moreover, if the Julia set $J_f$ of $f$ is connected, then it is locally connected at the Siegel boundary $\partial \Delta_f$.

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Jonguk Yang. 2020-10-27. Local Connectivity of Polynomial Julia sets at Bounded Type Siegel Boundaries. https://arxiv.org/abs/2010.14003

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