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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.21049 |
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| _version_ | 1866914993762467840 |
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| author | Davis, Caroline Mukundan, Malavika Stoll, Danny Tiozzo, Giulio |
| author_facet | Davis, Caroline Mukundan, Malavika Stoll, Danny Tiozzo, Giulio |
| contents | We describe a family $\textrm{Cyc}_p(\mathcal{F})$ of marked cycle curves that parameterize the cycles of period $p$ of a given family $\mathcal{F}$ of dynamical systems. We produce algorithms to compute a canonical cell decomposition for the marked cycle curves over the family $\textrm{Per}_1(0)$ of quadratic polynomials as well as over the family $\textrm{Per}_2(0)$ of quadratic rational maps with a critical 2-cycle. We obtain formulas for the number of $d$-cells in these decompositions, giving rise to e.g. a formula for their genus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21049 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A cell decomposition for marked cycle curves Davis, Caroline Mukundan, Malavika Stoll, Danny Tiozzo, Giulio Dynamical Systems 37F46, 37B10 We describe a family $\textrm{Cyc}_p(\mathcal{F})$ of marked cycle curves that parameterize the cycles of period $p$ of a given family $\mathcal{F}$ of dynamical systems. We produce algorithms to compute a canonical cell decomposition for the marked cycle curves over the family $\textrm{Per}_1(0)$ of quadratic polynomials as well as over the family $\textrm{Per}_2(0)$ of quadratic rational maps with a critical 2-cycle. We obtain formulas for the number of $d$-cells in these decompositions, giving rise to e.g. a formula for their genus. |
| title | A cell decomposition for marked cycle curves |
| topic | Dynamical Systems 37F46, 37B10 |
| url | https://arxiv.org/abs/2410.21049 |