Finite Dynamical Laminations
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917206425600000 |
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| author | Hilton, Forrest M. |
| author_facet | Hilton, Forrest M. |
| contents | We develop several combinatorial notions about laminations, some with clear implications for parameter space. We introduce a simplified class of laminations called finite dynamical laminations (FDL). In order to count FDL, we introduce sibling portraits, of which we provide a comprehensive counting theorem. We provide a characterization of which periodic polygons appear in invariant laminations. We introduce the pullback tree. The base of the pullback tree is a set of laminations, and we show that those laminations are proper and invariant, and all laminations in the base of the pullback tree correspond to a polynomial. We define the generational FDL graph, and it provides combinatorial information about polynomial parameter space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01353 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite Dynamical Laminations Hilton, Forrest M. Dynamical Systems Combinatorics 37F20 (Primary) 05A19 (Secondary) We develop several combinatorial notions about laminations, some with clear implications for parameter space. We introduce a simplified class of laminations called finite dynamical laminations (FDL). In order to count FDL, we introduce sibling portraits, of which we provide a comprehensive counting theorem. We provide a characterization of which periodic polygons appear in invariant laminations. We introduce the pullback tree. The base of the pullback tree is a set of laminations, and we show that those laminations are proper and invariant, and all laminations in the base of the pullback tree correspond to a polynomial. We define the generational FDL graph, and it provides combinatorial information about polynomial parameter space. |
| title | Finite Dynamical Laminations |
| topic | Dynamical Systems Combinatorics 37F20 (Primary) 05A19 (Secondary) |
| url | https://arxiv.org/abs/2408.01353 |