A model of the cubic connectedness locus
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909649374019584 |
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| author | Blokh, Alexander Oversteegen, Lex Timorin, Vladlen Wang, Yimin |
| author_facet | Blokh, Alexander Oversteegen, Lex Timorin, Vladlen Wang, Yimin |
| contents | We describe a locally connected model of the boundary of the cubic connectedness locus. The model is obtained by constructing a decomposition of the space of critical portraits and collapsing elements of the decomposition into points. This model is similar to a quotient of the quadratic combinatorial locus where all baby Mandelbrot sets are collapsed to points. All fibers of the model, possibly except one, are connected. This paper is dedicated to the memory of Yuri Ilyich Lyubich. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_11516 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A model of the cubic connectedness locus Blokh, Alexander Oversteegen, Lex Timorin, Vladlen Wang, Yimin Dynamical Systems Primary 37F20, 37F10, Secondary 37F25 We describe a locally connected model of the boundary of the cubic connectedness locus. The model is obtained by constructing a decomposition of the space of critical portraits and collapsing elements of the decomposition into points. This model is similar to a quotient of the quadratic combinatorial locus where all baby Mandelbrot sets are collapsed to points. All fibers of the model, possibly except one, are connected. This paper is dedicated to the memory of Yuri Ilyich Lyubich. |
| title | A model of the cubic connectedness locus |
| topic | Dynamical Systems Primary 37F20, 37F10, Secondary 37F25 |
| url | https://arxiv.org/abs/2304.11516 |