Abstract
We show that the tangential speed \(v^T_\phi (t)\) of a parabolic semigroup \((\phi _t)\) of holomorphic self-maps in the unit disc is asymptotically bounded from above by \((1/2)\log t\), 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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Notes
In the following, we will only write starlike at infinity assuming that we have chosen this direction.
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Partially supported by PRIN Real and Complex Manifolds: Topology, Geometry and holomorphic dynamics n. 2017JZ2SW5 and by the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006.
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Cordella, D. Asymptotic upper bound for tangential speed of parabolic semigroups of holomorphic self-maps in the unit disc. Annali di Matematica 200, 2767–2784 (2021). https://doi.org/10.1007/s10231-021-01100-x
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DOI: https://doi.org/10.1007/s10231-021-01100-x