| Autor: |
Lazebnik, Kirill, Makarov, Nikolai G., Mukherjee, Sabyasachi |
| Rok vydání: |
2019 |
| Předmět: |
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| Zdroj: |
Trans. Amer. Math. Soc. 374 (2021), 4839-4893 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1090/tran/8387 |
| Popis: |
We study rational functions $f$ of degree $d+1$ such that $f$ is univalent in the exterior unit disc, and the image of the unit circle under $f$ has the maximal number of cusps ($d+1$) and double points $(d-2)$. We introduce a bi-angled tree associated to any such $f$. It is proven that any bi-angled tree is realizable by such an $f$, and moreover, $f$ is essentially uniquely determined by its associated bi-angled tree. This combinatorial classification is used to show that such $f$ are in natural 1:1 correspondence with anti-holomorphic polynomials of degree $d$ with $d-1$ distinct, fixed critical points (classified by their Hubbard trees). |
| Databáze: |
arXiv |
| Externí odkaz: |
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