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28 March 2024
 
  » arxiv » 1908.5813

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Univalent Polynomials and Hubbard Trees
Kirill Lazebnik ; Nikolai G. Makarov ; Sabyasachi Mukherjee ;
Date 16 Aug 2019
AbstractWe study rational functions $f$ of degree $d$, univalent in the exterior unit disc, with $f(mathbb{T})$ having 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. We connect this class of rational maps and their associated bi-angled trees to the class of anti-holomorphic polynomials of degree $d$ with $d-1$ distinct, fixed critical points and their associated Hubbard trees.
Source arXiv, 1908.5813
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