Trajectories of semigroups of holomorphic functions and harmonic measure
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 $ [π/2,-π/2] $. The same method is used for the slope of a backward trajectory approaching a super-repulsive fixed point.
math.CV↗