Lemon limbs of the cubic connectedness locus
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911158086139904 |
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| author | Petersen, Carsten Lunde Zakeri, Saeed |
| author_facet | Petersen, Carsten Lunde Zakeri, Saeed |
| contents | We describe a primary limb structure in the connectedness locus of complex cubic polynomials, where the limbs are indexed by the periodic points of the doubling map $t \mapsto 2t \ (\operatorname{mod} {\mathbb Z})$. The main renormalization locus in each limb is parametrized by the product of a pair of (punctured) Mandelbrot sets. This parametrization is the inverse of the straightening map and can be thought of as a tuning operation that manufactures a unique cubic of a given combinatorics from a pair of quadratic hybrid classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19081 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lemon limbs of the cubic connectedness locus Petersen, Carsten Lunde Zakeri, Saeed Dynamical Systems 37F10, 37F20, 37F25, 37F31, 37F46 We describe a primary limb structure in the connectedness locus of complex cubic polynomials, where the limbs are indexed by the periodic points of the doubling map $t \mapsto 2t \ (\operatorname{mod} {\mathbb Z})$. The main renormalization locus in each limb is parametrized by the product of a pair of (punctured) Mandelbrot sets. This parametrization is the inverse of the straightening map and can be thought of as a tuning operation that manufactures a unique cubic of a given combinatorics from a pair of quadratic hybrid classes. |
| title | Lemon limbs of the cubic connectedness locus |
| topic | Dynamical Systems 37F10, 37F20, 37F25, 37F31, 37F46 |
| url | https://arxiv.org/abs/2504.19081 |