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arXiv · 1902.03426

Trajectories of semigroups of holomorphic functions and harmonic measure

Georgios Kelgiannis
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Abstract

We give an explicit relation between the slope of the trajectory of a semigroup of holomorphic functions and the harmonic measure of the associated planar domain ${\varOmega}$. We use this to construct a semigroup whose slope is an arbitrary interval in $ [{\pi}/2,-{\pi}/2] $. The same method is used for the slope of a backward trajectory approaching a super-repulsive fixed point.

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Georgios Kelgiannis. 2019-02-09. Trajectories of semigroups of holomorphic functions and harmonic measure. https://doi.org/10.1016/j.jmaa.2019.02.024

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