Quasiconformal Surgery in Holomorphic Dynamics

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Bodil Branner (Technical University of Denmark, Lyngby) Núria Fagella (Universitat de Barcelona)

Quasiconformal Surgery in Holomorphic Dynamics

Bodil Branner (Technical University of Denmark, Lyngby), Núria Fagella (Universitat de Barcelona)

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English

Cambridge University Press
23 January 2014

Mathematics; Real analysis, real variables; Complex analysis, complex variables; Geometry

Series: Cambridge Studies in Advanced Mathematics

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.

By: Bodil Branner (Technical University of Denmark Lyngby), Núria Fagella (Universitat de Barcelona)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 141
Dimensions: Height: 233mm, Width: 156mm, Spine: 20mm
Weight: 850g
ISBN: 9781107042919
ISBN 10: 1107042917
Series: Cambridge Studies in Advanced Mathematics
Pages: 428
Publication Date: 23 January 2014
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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 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.

Reviews for Quasiconformal Surgery in Holomorphic Dynamics

'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