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Continuous semigroups of holomorphic...

Bracci, Filippo.

Continuous semigroups of holomorphic self-maps of the unit disc

Record Type:	Electronic resources : Monograph/item
Title/Author:	Continuous semigroups of holomorphic self-maps of the unit discby Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal.
Author:	Bracci, Filippo.
other author:	Contreras, Manuel D.
Published:	Cham :Springer International Publishing :2020.
Description:	xxvii, 566 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Semigroups.
Online resource:	https://doi.org/10.1007/978-3-030-36782-4
ISBN:	9783030367824$q(electronic bk.)

Continuous semigroups of holomorphic self-maps of the unit disc
Bracci, Filippo.

Continuous semigroups of holomorphic self-maps of the unit disc[electronic resource] /by Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal. - Cham :Springer International Publishing :2020. - xxvii, 566 p. :ill., digital ;24 cm. - Springer monographs in mathematics,1439-7382. - Springer monographs in mathematics..

Part I: Preliminaries -- 1 Hyperbolic geometry and interation -- 2. Holomorphic functions with non-negative real part -- 3. Univalent functions -- 4. Caratheodory'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.

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 Caratheodory 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.

ISBN: 9783030367824$q(electronic bk.)

Standard No.: 10.1007/978-3-030-36782-4doiSubjects--Topical Terms:

239334
Semigroups.

LC Class. No.: QA182 / .B733 2020

Dewey Class. No.: 515.9

Continuous semigroups of holomorphic self-maps of the unit disc
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505 0 $a Part I: Preliminaries -- 1 Hyperbolic geometry and interation -- 2. Holomorphic functions with non-negative real part -- 3. Univalent functions -- 4. Caratheodory'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.
520 $a 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 Caratheodory 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.
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