Continuous Semigroups of Holomorphic Self-maps of the Unit Disc

Download or read book Continuous Semigroups of Holomorphic Self-maps of the Unit Disc written by Filippo Bracci and published by Springer Nature. This book was released on 2020-02-14 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.