Overview
- 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
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (18 chapters)
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Front Matter
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Semigroups
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Front Matter
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Keywords
About this book
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.
Reviews
Authors and Affiliations
About the authors
Prof. Filippo Bracci obtained his PhD in Mathematics at the University of Padova in 2001. He is full professor at the University of Rome Tor Vergata since 2007. He was the principal investigator of the ERC project “HEVO”. His research interests include complex analysis, several complex variables and holomorphic dynamics.
Prof. Manuel D. Contreras obtained his Ph.D. in Mathematics at the Universidad de Granada in 1993. He is full professor at Departamento de Matemática Aplicada II of the Universidad de Sevilla. His main research interests are complex analysis, geometric function theory, holomorphic dynamics, spaces of analytic functions and operators acting on them.
Prof. Santiago Díaz-Madrigal obtained his Ph.D. in Mathematics at the Universidad de Sevilla in 1990. He is a full professor at Universidad de Sevilla in the department of Matemática Aplicada II since 1998. His current research interests include complex analysis, dynamical systems and probability and, especially, those areas where these topics interact with each other.
Bibliographic Information
Book Title: Continuous Semigroups of Holomorphic Self-maps of the Unit Disc
Authors: Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-030-36782-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-36781-7Published: 15 February 2020
Softcover ISBN: 978-3-030-36784-8Published: 15 February 2021
eBook ISBN: 978-3-030-36782-4Published: 14 February 2020
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XXVII, 566
Number of Illustrations: 18 b/w illustrations
Topics: Functions of a Complex Variable, Dynamical Systems and Ergodic Theory, Functional Analysis, Ordinary Differential Equations, Geometry