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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埋葬

Models and Koenigs Functionsorbits of a semigroup or abstract basin of attraction) which inherits a complex structure of simply connected Riemann surface, in such a way that the semigroup is conjugated to a continuous group of automorphisms of such a Riemann surface. Moreover, our construction is universal, which implies that

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Mutter

Extension to the Boundarynd 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

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Contact Pointschapter we examine the other points, which turn out to be contact points, and we show that super-repelling fixed points can be divided into two separated sets: those which are the landing point of a backward orbit and those which are the initial point of a maximal contact arc (in the latter case the

Sad570

Poles of the Infinitesimal Generators terms of .-points (. pre-images of values with a positive (Carleson-Makarov) .-numbers) of the associated semigroup and of the associated Koenigs function. We also define a natural duality operation in the cone of infinitesimal generators and show that the regular poles of an infinitesimal generato