Trajectories of semigroups of holomorphic functions and harmonic measure

Georgios Kelgiannis

doi:10.1016/j.jmaa.2019.02.024

paper

Trajectories of semigroups of holomorphic functions and harmonic measure

arXiv:1902.03426 · doi:10.1016/j.jmaa.2019.02.024

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 $Ω$ . We use this to construct a semigroup whose slope is an arbitrary interval in $[π /2, - π /2]$ . The same method is used for the slope of a backward trajectory approaching a super-repulsive fixed point.

12 pages, 1 figure