Trajectories of semigroups of holomorphic functions and harmonic measure
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 . 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.
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