Format:
1 Online-Ressource (XXVII, 566 Seiten)
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Illustrationen
ISBN:
9783030367824
Series Statement:
Springer Monographs in Mathematics
Content:
Part I: Preliminaries -- 1 Hyperbolic geometry and interation -- 2. Holomorphic functions with non-negative real part -- 3. Univalent functions -- 4. Carathéodory’s prime ends theory -- 5. Hyperbolic geometry in simply connected domains -- 6. Quasi-geodesics and localization -- 7. Harmonic measures and Bloch functions -- Part II: Semigroups -- 8 Semigroups of holomorphic functions -- 9 Models and Koenigs functions -- 10 Infinitesimal generators -- 11 Extension to the boundary -- 12 Boundary fixed points and infinitesimal generators -- 13 Fixed points, backward invariant sets and petals -- 14 Contact points -- 15 Poles of the infinitesimal generators -- 16 Rate of convergence at the Denjoy-Wolffpoint -- 17 Slopes of orbits at the Denjoy-Wolffpoint -- 18 Topological invariants.
Content:
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 proved in details.
Additional Edition:
ISBN 9783030367817
Additional Edition:
ISBN 9783030367831
Additional Edition:
ISBN 9783030367848
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783030367817
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783030367831
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783030367848
Language:
English
DOI:
10.1007/978-3-030-36782-4
Author information:
Bracci, Filippo 1973-
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