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Angular extents and trajectory slopes in the theory of holomorphic semigroups in the unit disk (2010.01883v1)
Published 5 Oct 2020 in math.CV and math.DS
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.