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Quasiconformal Surgery in Holomorphic Dynamics


Part of Cambridge Studies in Advanced Mathematics

Xavier Buff, Christian Henriksen, Shaun Bullett, Adam L. Epstein, Michael Yampolsky, Peter Haïssinsky, Carsten L. Petersen, Kevin M. Pilgrim, Tan Lei
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  • Date Published: January 2014
  • availability: In stock
  • format: Hardback
  • isbn: 9781107042919

£ 72.99

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About the Authors
  • 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.

    • The first one-stop text for learning the technique of quasiconformal surgery
    • Numerous illustrations lead the reader to a better understanding of the geometrical ideas behind the proofs
    • Includes contributions from leading experts in their field
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    Reviews & endorsements

    'This worthwhile book, written by two of the main experts in this field with some contributions from some well-known researchers, gives a comprehensive introduction to the subject, from the foundations of the theory up to several important and representative applications … All in all, this book is a very welcome addition to the literature, and an excellent entrance point to the theory for any researcher interested in this subject.' Marco Abate, Zentralblatt MATH

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    Product details

    • Date Published: January 2014
    • format: Hardback
    • isbn: 9781107042919
    • length: 428 pages
    • dimensions: 233 x 156 x 20 mm
    • weight: 0.84kg
    • contains: 30 b/w illus. 105 colour illus. 85 exercises
    • availability: In stock
  • Table of Contents

    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
    Symbol index

  • Authors

    Bodil Branner, Technical University of Denmark, Lyngby
    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.

    Núria Fagella, Universitat de Barcelona
    Núria Fagella is currently Associate Professor at Universitat de Barcelona. Her research is in the area of holomorphic dynamics with an emphasis on the iteration of transcendental functions. She publishes in renowned international journals and with a diverse range of collaborators worldwide. Fagella has been invited to deliver talks and short courses at numerous international conferences and workshops, and has been an organiser of several such events.


    Xavier Buff, Christian Henriksen, Shaun Bullett, Adam L. Epstein, Michael Yampolsky, Peter Haïssinsky, Carsten L. Petersen, Kevin M. Pilgrim, Tan Lei

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