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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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书目名称Continuous Semigroups of Holomorphic Self-maps of the Unit Disc
编辑Filippo Bracci,Manuel D. Contreras,Santiago Díaz-M
视频video
概述Complete updated self-contained book on the theory of semigroups.Can be used as a reference source for researchers and as an introductory book for graduate students in complex analysis and iteration t
丛书名称Springer Monographs in Mathematics
图书封面Titlebook: Continuous Semigroups of Holomorphic Self-maps of the Unit Disc;  Filippo Bracci,Manuel D. Contreras,Santiago Díaz-M Book 2020 Springer Nat
描述The book faces the interplay among dynamical properties of semigroups, analytical properties of infinitesimal generators and geometrical properties of Koenigs functions. .The book includes precise descriptions of the behavior of trajectories, backward orbits, petals and boundary behavior in general, aiming to give a rather complete picture of all interesting phenomena that occur. In order to fulfill this task, we choose to introduce a new point of view, which is mainly based on the intrinsic dynamical aspects of semigroups in relation with the hyperbolic distance and a deep use of Carathéodory prime ends topology and Gromov hyperbolicity theory. .This work is intended both as a reference source for researchers interested in the subject, and as an introductory book for beginners with a (undergraduate) background in real and complex analysis. For this purpose, the book is self-contained and all non-standard (and, mostly, all standard) results are provedin details..
出版日期Book 2020
关键词Semigroups of holomorphic functions; Univalent functions; Hyperbolic metric; Iteration theory; Holomorph
版次1
doihttps://doi.org/10.1007/978-3-030-36782-4
isbn_softcover978-3-030-36784-8
isbn_ebook978-3-030-36782-4Series ISSN 1439-7382 Series E-ISSN 2196-9922
issn_series 1439-7382
copyrightSpringer Nature Switzerland AG 2020
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Poles of the Infinitesimal Generatorsr correspond to the regular critical points of the dual generator. Finally we apply such a construction to study radial multi-slits and give an example of a non-isolated radial slit semigroup whose tip has not a positive (Carleson-Makarov) .-number.
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1439-7382 ok for graduate students in complex analysis and iteration tThe book faces the interplay among dynamical properties of semigroups, analytical properties of infinitesimal generators and geometrical properties of Koenigs functions. .The book includes precise descriptions of the behavior of trajectorie
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https://doi.org/10.1007/978-3-322-87097-1 prove the No Koebe Arcs Theorem, from which we obtain several results about pre-images of slits via univalent maps. Then we present the so-called Koebe Distortion Theorems. Finally, we consider families of univalent functions and prove the Carathéodory Kernel Convergence Theorem.
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Manfred Müller-Gransee,Rolf Wabner is essentially impossible to detect geodesics in simply connected domains, we introduce the notion of Gromov’s ., which are usually much simpler to find, and prove the so-called ., which states that close to every quasi-geodesic there is a geodesic.
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Rudolf Manz,Claude Lichtenstein holomorphic vector field in the unit disc, its infinitesimal generator. Once shown the existence of such a vector field, we will focus on different descriptions and characterizations of infinitesimal generators and discuss several of their properties and examples.
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https://doi.org/10.1007/978-3-322-87189-3e non-tangential limit at every boundary point. Moreover, the semigroup functional equation and the functional equation defined by the canonical model extend in the non-tangential limits sense up to the boundary. In the last part of the chapter we analyze conditions for a . continuous extension of iterates of a semigroup up to the boundary.
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