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| Format: | Preprint |
| Veröffentlicht: |
2022
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2202.09832 |
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| _version_ | 1866908552952545280 |
|---|---|
| author | Calegari, Danny |
| author_facet | Calegari, Danny |
| contents | We introduce an analog in the context of rational maps of the idea of hyperbolic Dehn surgery from the theory of Kleinian groups. A surgery sequence is a sequence of postcritically finite maps limiting (in a precise manner) to a postcritically finite map with at least one strictly preperiodic critical orbit. As an application of this idea we give a new and elementary proof of Tan Lei's theorem on the asymptotic self-similarity of Julia Sets and the Mandelbrot Set at Misiurewicz points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_09832 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Surgery sequences and self-similarity of the Mandelbrot set Calegari, Danny Dynamical Systems We introduce an analog in the context of rational maps of the idea of hyperbolic Dehn surgery from the theory of Kleinian groups. A surgery sequence is a sequence of postcritically finite maps limiting (in a precise manner) to a postcritically finite map with at least one strictly preperiodic critical orbit. As an application of this idea we give a new and elementary proof of Tan Lei's theorem on the asymptotic self-similarity of Julia Sets and the Mandelbrot Set at Misiurewicz points. |
| title | Surgery sequences and self-similarity of the Mandelbrot set |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2202.09832 |