Titlebook: Continuous Semigroups of Holomorphic Self-maps of the Unit Disc; Filippo Bracci,Manuel D. Contreras,Santiago Díaz-M Book 2020 Springer Nat

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Rate of Convergence at the Denjoy-Wolff Pointh “orthogonal speed” and “total speed” as introduced in Definition .. As we see, in the hyperbolic case the speed of convergence follows strict rules, while, in the parabolic case the situation is more complicated.

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Rudolf Manz,Claude Lichtensteinsemigroup: the infinitesimal generator. We see how to relate semigroups to Cauchy problems, showing that every semigroup is completely determined by a holomorphic vector field in the unit disc, its infinitesimal generator. Once shown the existence of such a vector field, we will focus on different d

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https://doi.org/10.1007/978-3-322-87189-3nd the principal part of prime ends of domains defined by Koenigs functions, we prove that every Koenigs function and every iterate of a semigroup have non-tangential limit at every boundary point. Moreover, the semigroup functional equation and the functional equation defined by the canonical model