Univalent polynomials and Hubbard trees

  title={Univalent polynomials and Hubbard trees},
  author={Kirill Lazebnik and Nikolai G. Makarov and Sabyasachi Mukherjee},
  journal={Transactions of the American Mathematical Society},
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… 
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  • K. Lazebnik
  • Mathematics
    Conformal Geometry and Dynamics of the American Mathematical Society
  • 2021
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