English

Angular extents and trajectory slopes in the theory of holomorphic semigroups in the unit disk

Complex Variables 2020-10-06 v1 Dynamical Systems

Abstract

We study relationships between the asymptotic behaviour of a non-elliptic semigroup of holomorphic self-maps of the unit disk and the geometry of its planar domain (the image of the Koenigs function). We establish a sufficient condition for the trajectories of the semigroup to converge to its Denjoy-Wolff point with a definite slope. We obtain as a corollary two previously known sufficient conditions.

Keywords

Cite

@article{arxiv.2010.01883,
  title  = {Angular extents and trajectory slopes in the theory of holomorphic semigroups in the unit disk},
  author = {Manuel D. Contreras and Santiago Díaz-Madrigal and Pavel Gumenyuk},
  journal= {arXiv preprint arXiv:2010.01883},
  year   = {2020}
}