Continuous Semigroups of Holomorphic Self-maps of the Unit Disc

Beschreibung

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.
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.
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 theory Includes detailed chapters developing the Carathéodory prime ends topology and on Gromov hyperbolicity theory in simply connected domains

Autor*in

Filippo Bracci

Themen in »Continuous Semigroups of Holomorphic Self-maps of the Unit Disc«

Semigroups of holomorphic functions Univalent functions Hyperbolic metric Iteration theory Holomorphic ODE ordinary differential equations

Stimmen zu »Continuous Semigroups of Holomorphic Self-maps of the Unit Disc«

“This monograph contains a collection of results from the majority of works in the field of continuous semigroups and that it is a valuable manual for researchers working in this vast area.” (Maria Kourou, Mathematical Reviews, September, 2022)
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