Julia sets appear quasiconformally in the Mandelbrot set, II: A parabolic proof
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908571934916608 |
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| author | Kawahira, Tomoki Kisaka, Masashi |
| author_facet | Kawahira, Tomoki Kisaka, Masashi |
| contents | Following the ideas of A.~Douady, we give an alternative proof of the authors' result: for any boundary point $c_0$ of the Mandelbrot set $M$, we can find small quasiconformal copies of $M$ in $M$ that are encaged in nested quasiconformal copies of the totally disconnected Julia set of a parameter arbitrarily close to $c_0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01013 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Julia sets appear quasiconformally in the Mandelbrot set, II: A parabolic proof Kawahira, Tomoki Kisaka, Masashi Dynamical Systems Complex Variables Primary 37F46 Secondary 37F25, 37F31 Following the ideas of A.~Douady, we give an alternative proof of the authors' result: for any boundary point $c_0$ of the Mandelbrot set $M$, we can find small quasiconformal copies of $M$ in $M$ that are encaged in nested quasiconformal copies of the totally disconnected Julia set of a parameter arbitrarily close to $c_0$. |
| title | Julia sets appear quasiconformally in the Mandelbrot set, II: A parabolic proof |
| topic | Dynamical Systems Complex Variables Primary 37F46 Secondary 37F25, 37F31 |
| url | https://arxiv.org/abs/2510.01013 |