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  3. Quasiconformal Surgery in Holomorphic Dynamics
  • Cited by 46
Publisher:
Cambridge University Press
Online publication date:
February 2014
Print publication year:
2014
Online ISBN:
9781107337602
DOI:
https://doi.org/10.1017/CBO9781107337602
Subjects:
Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Real and Complex Analysis
Series:
Cambridge Studies in Advanced Mathematics (141)
Information

Book description

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.

Reviews

'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 Source: Zentralblatt MATH

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Contents

Contents
References
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