Sierpinski carpet hyperbolic components of disjoint type are bounded
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918151411728384 |
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| author | Dudko, Dzimitry Luo, Yusheng |
| author_facet | Dudko, Dzimitry Luo, Yusheng |
| contents | We establish certain uniform a priori bounds for hyperbolic components of disjoint type. As an application, we will prove that Sierpinski carpet hyperbolic components of disjoint type are bounded. Furthermore, we show that for each map $f$ on the closure of such a hyperbolic component, there exists a quadratic-like restriction around every non-repelling periodic point. Extensions of these results to non-Sierpinski configurations are underway. As a prototype example, we describe the post-critical set of any map on the boundary of the hyperbolic component of $z^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25658 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sierpinski carpet hyperbolic components of disjoint type are bounded Dudko, Dzimitry Luo, Yusheng Dynamical Systems Complex Variables Geometric Topology 30C10, 37F05, 37F10, 37F32, 37F34 We establish certain uniform a priori bounds for hyperbolic components of disjoint type. As an application, we will prove that Sierpinski carpet hyperbolic components of disjoint type are bounded. Furthermore, we show that for each map $f$ on the closure of such a hyperbolic component, there exists a quadratic-like restriction around every non-repelling periodic point. Extensions of these results to non-Sierpinski configurations are underway. As a prototype example, we describe the post-critical set of any map on the boundary of the hyperbolic component of $z^2$. |
| title | Sierpinski carpet hyperbolic components of disjoint type are bounded |
| topic | Dynamical Systems Complex Variables Geometric Topology 30C10, 37F05, 37F10, 37F32, 37F34 |
| url | https://arxiv.org/abs/2509.25658 |