Boundary of the central hyperbolic component I: dynamical properties
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916806702137344 |
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| author | Cao, Jie Wang, Xiaoguang Yin, Yongcheng |
| author_facet | Cao, Jie Wang, Xiaoguang Yin, Yongcheng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18487 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary of the central hyperbolic component I: dynamical properties Cao, Jie Wang, Xiaoguang Yin, Yongcheng Dynamical Systems 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. |
| title | Boundary of the central hyperbolic component I: dynamical properties |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2506.18487 |