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Article overview
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Univalent Polynomials and Hubbard Trees | Kirill Lazebnik
; Nikolai G. Makarov
; Sabyasachi Mukherjee
; | Date: |
16 Aug 2019 | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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