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arXiv · 2210.14305

Parabolic Components in Cubic Polynomial Slice $Per_1(1)$

Runze Zhang
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Abstract

We prove that the boundary of every parabolic component in the cubic polynomial slice $Per_1(1)$ is a Jordan curve by adapting the technique of para-puzzles presented in \cite{Roesch1}. We also give a global description of the connected locus $\mathcal{C}_1$: it is the union of two main parabolic components and the limbs attached on their boundaries.

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Runze Zhang. 2022-10-25. Parabolic Components in Cubic Polynomial Slice $Per_1(1)$. https://arxiv.org/abs/2210.14305

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