Springer Monographs in Mathematics

Continuous Semigroups of Holomorphic Self-maps of the Unit Disc

Authors: Bracci, Filippo, Contreras, Manuel D., Diaz-Madrigal, Santiago

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  • 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
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eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-030-36782-4
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  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-3-030-36781-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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.

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.

Table of contents (18 chapters)

Table of contents (18 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-030-36782-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-3-030-36781-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Continuous Semigroups of Holomorphic Self-maps of the Unit Disc
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-36782-4
DOI
10.1007/978-3-030-36782-4
Hardcover ISBN
978-3-030-36781-7
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XXVII, 566
Number of Illustrations
18 b/w illustrations
Topics