M. D. Contreras, S. Díaz-Madrigal, P. Gumenyuk

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

J. Geom. Analysis, 31(11):10603-10633, 2021.
DOI: 10.1007/s12220-021-00659-4

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.

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