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Continuous Semigroups of Holomorphic Self-maps of the Unit Disc

  • Filippo Bracci
  • Manuel D. Contreras
  • Santiago Díaz-Madrigal
Book
  • 597 Downloads

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xxvii
  2. Preliminaries

    1. Front Matter
      Pages 1-1
    2. Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
      Pages 3-58
    3. Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
      Pages 59-70
    4. Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
      Pages 71-90
    5. Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
      Pages 91-115
    6. Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
      Pages 117-132
    7. Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
      Pages 133-169
    8. Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
      Pages 171-201
  3. Semigroups

    1. Front Matter
      Pages 203-203
    2. Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
      Pages 205-228
    3. Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
      Pages 229-272
    4. Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
      Pages 273-306
    5. Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
      Pages 307-325
    6. Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
      Pages 327-354
    7. Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
      Pages 355-406
    8. Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
      Pages 407-427
    9. Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
      Pages 429-451
    10. Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
      Pages 453-480
    11. Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
      Pages 481-539
    12. Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal
      Pages 541-555
  4. Back Matter
    Pages 557-566

About this book

Introduction

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.

Keywords

Semigroups of holomorphic functions Univalent functions Hyperbolic metric Iteration theory Holomorphic ODE

Authors and affiliations

  • Filippo Bracci
    • 1
  • Manuel D. Contreras
    • 2
  • Santiago Díaz-Madrigal
    • 3
  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly
  2. 2.Departamento de Matemática Aplicada II and IMUSUniversidad de SevillaSevillaSpain
  3. 3.Departamento de Matemática Aplicada II and IMUSUniversidad de SevillaSevillaSpain

Bibliographic information

  • 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
  • Buy this book on publisher's site