Boundary of the central hyperbolic component II: boundary extension theorem
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915485937827840 |
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| author | Cao, Jie Wang, Xiaoguang Yin, Yongcheng |
| author_facet | Cao, Jie Wang, Xiaoguang Yin, Yongcheng |
| contents | In this paper, we study the boundary behavior of Milnor's parameterization $Φ: \mathcal B_d\rightarrow \mathcal H_d$ of the central hyperbolic component $\mathcal H_d$ via Blaschke products. We establish a boundary extension theorem by giving a necessary and sufficient condition for $D\in \partial \mathcal B_d$ which allows $Φ$-extension. Further we show that cusps are dense in a full Hausdorff dimensional subset of $\partial \mathcal H_d$, partially confirming a conjecture of McMullen. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07350 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary of the central hyperbolic component II: boundary extension theorem Cao, Jie Wang, Xiaoguang Yin, Yongcheng Dynamical Systems Complex Variables In this paper, we study the boundary behavior of Milnor's parameterization $Φ: \mathcal B_d\rightarrow \mathcal H_d$ of the central hyperbolic component $\mathcal H_d$ via Blaschke products. We establish a boundary extension theorem by giving a necessary and sufficient condition for $D\in \partial \mathcal B_d$ which allows $Φ$-extension. Further we show that cusps are dense in a full Hausdorff dimensional subset of $\partial \mathcal H_d$, partially confirming a conjecture of McMullen. |
| title | Boundary of the central hyperbolic component II: boundary extension theorem |
| topic | Dynamical Systems Complex Variables |
| url | https://arxiv.org/abs/2509.07350 |