Abstract
We show that the tangential speed of a parabolic semigroup of holomorphic self-maps in the unit disc is asymptotically bounded from above by (1/2)logt, proving a conjecture by Bracci. In order to show the proof we need a result of "asymptotical monotonicity" of the tangential speed for proper pairs of parabolic semigroups with positive hyperbolic step.
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