About this book
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.
Semigroups of holomorphic functions Univalent functions Hyperbolic metric Iteration theory Holomorphic ODE
- DOI https://doi.org/10.1007/978-3-030-36782-4
- Copyright Information Springer Nature Switzerland AG 2020
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-030-36781-7
- Online ISBN 978-3-030-36782-4
- Series Print ISSN 1439-7382
- Series Online ISSN 2196-9922
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