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arXiv · 2506.18487

Boundary of the central hyperbolic component I: dynamical properties

Jie Cao·Xiaoguang Wang·Yongcheng Yin
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Abstract

We study the dynamics of polynomial maps on the boundary of the central hyperbolic component $\mathcal H_d$. We prove the local connectivity of Julia sets and a rigidity theorem for maps on the regular part of $\partial\mathcal H_d$. Our proof is based on the construction of Fatou trees and employs the puzzle technique as a key methodological framework. These results are applicable to a larger class of maps for which the maximal Fatou trees equal the filled Julia sets.

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Jie Cao, Xiaoguang Wang, Yongcheng Yin. 2025-06-23. Boundary of the central hyperbolic component I: dynamical properties. https://arxiv.org/abs/2506.18487

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