The angular derivative problem for petals of one-parameter semigroups in the unit disk

  • Pavel Gumenyuk

    Politecnico di Milano, Italy
  • Maria Kourou

    Julius-Maximilians University of Würzburg, Germany
  • Oliver Roth

    Julius-Maximilians University of Würzburg, Germany
The angular derivative problem for petals of one-parameter semigroups in the unit disk cover
Download PDF

A subscription is required to access this article.

Abstract

We study the angular derivative problem for petals of one-parameter semigroups of holomorphic self-maps of the unit disk. For hyperbolic petals, we prove a necessary and sufficient condition for the conformality of the petal in terms of the intrinsic hyperbolic geometry of the petal and the backward dynamics of the semigroup. For parabolic petals, we characterize conformality of the petal in terms of the asymptotic behaviour of the Koenigs function at the Denjoy–Wolff point.

Cite this article

Pavel Gumenyuk, Maria Kourou, Oliver Roth, The angular derivative problem for petals of one-parameter semigroups in the unit disk. Rev. Mat. Iberoam. (2024), published online first

DOI 10.4171/RMI/1460