Angular extents and trajectory slopes in the theory of holomorphic semigroups in the unit disk
- Resource Type
- Working Paper
- Authors
- Contreras, Manuel D.; Díaz-Madrigal, Santiago; Gumenyuk, Pavel
- Source
- Subject
- Mathematics - Complex Variables
Mathematics - Dynamical Systems
Primary: 30D05, Secondary: 30C35, 30C45, 34M15
- Language
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.