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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2503.08868 |
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| _version_ | 1866917952110985216 |
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| author | Bonifant, Araceli Milnor, John |
| author_facet | Bonifant, Araceli Milnor, John |
| contents | We study the parameter space ${\mathcal S}_p$ for cubic polynomial maps with a marked critical point of period $p$. We will outline a fairly complete theory as to how the dynamics of the map $F$ changes as we move around the parameter space ${\mathcal S}_p$. For every escape region ${\mathcal E}\subset {\mathcal S}_p$, every parameter ray in ${\mathcal E}$ with rational parameter angle lands at some uniquely defined point in the boundary $\partial{\mathcal E}$. This landing point is necessarily either a parabolic map or a Misiurewicz map. The relationship between parameter rays and dynamic rays is formalized by the period $q$ tessellation of ${\mathcal S}_p$, where maps in the same face of this tessellation always have the same period $q$ orbit portrait. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08868 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cubic Polynomial Maps with Periodic Critical Orbit, Part III: Tessellations and Orbit Portraits Bonifant, Araceli Milnor, John Dynamical Systems 37F10, 30C10, 30D05 We study the parameter space ${\mathcal S}_p$ for cubic polynomial maps with a marked critical point of period $p$. We will outline a fairly complete theory as to how the dynamics of the map $F$ changes as we move around the parameter space ${\mathcal S}_p$. For every escape region ${\mathcal E}\subset {\mathcal S}_p$, every parameter ray in ${\mathcal E}$ with rational parameter angle lands at some uniquely defined point in the boundary $\partial{\mathcal E}$. This landing point is necessarily either a parabolic map or a Misiurewicz map. The relationship between parameter rays and dynamic rays is formalized by the period $q$ tessellation of ${\mathcal S}_p$, where maps in the same face of this tessellation always have the same period $q$ orbit portrait. |
| title | Cubic Polynomial Maps with Periodic Critical Orbit, Part III: Tessellations and Orbit Portraits |
| topic | Dynamical Systems 37F10, 30C10, 30D05 |
| url | https://arxiv.org/abs/2503.08868 |