Bodil Branner

Quasiconformal Surgery in Holomorphic Dynamics (eBook, PDF)

• Format: PDF

Produktbeschreibung

Since its introduction in the early 1980s quasiconformal surgery has become a major tool in the development of the theory of holomorphic dynamics, and it is essential background knowledge for any researcher in the field. In this comprehensive introduction the authors begin with the foundations and a general description of surgery techniques before turning their attention to a wide variety of applications. They demonstrate the different types of surgeries that lie behind many important results in holomorphic dynamics, dealing in particular with Julia sets and the Mandelbrot set. Two of these surgeries go beyond the classical realm of quasiconformal surgery and use trans-quasiconformal surgery. Another deals with holomorphic correspondences, a natural generalization of holomorphic maps. The book is ideal for graduate students and researchers requiring a self-contained text including a variety of applications. It particularly emphasises the geometrical ideas behind the proofs, with many helpful illustrations seldom found in the literature.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 23. Januar 2014
• Englisch
• ISBN-13: 9781107597204
• Artikelnr.: 40296267

Autorenporträt

Bodil Branner is Professor Emerita at the Technical University of Denmark, Lyngby. Her research interests include holomorphic dynamics and complex analysis. She has published in several renowned international journals and given numerous invited talks at conferences, workshops and symposia. Branner has served as Vice-President of the European Mathematical Society, as President of Dansk Matematisk Forening (DMF) and she was one of the founders of European Women in Mathematics. She is an honorary member of DMF and a Fellow of the AMS.

Inhaltsangabe

Preface
Introduction
1. Quasiconformal geometry
2. Extensions and interpolations
3. Preliminaries on dynamical systems and actions of Kleinian groups
4. Introduction to surgery and first occurrences
5. General principles of surgery
6. Soft surgeries with a contribution by X. Buff and C. Henriksen
7. Cut and paste surgeries with contributions by K. M. Pilgrim, Tan Lei and S. Bullett
8. Cut and paste surgeries with sectors with a contribution by A. L. Epstein and M. Yampolsky
9. Trans-quasiconformal surgery with contributions by C. L. Petersen and P. Haïssinsky
Bibliography
Symbol index
Index.