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Quasiconformal surgery in holomorphi...

Branner, Bodil.

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Quasiconformal surgery in holomorphic dynamics

Record Type:	Electronic resources : Monograph/item
Title/Author:	Quasiconformal surgery in holomorphic dynamics/ Bodil Branner and Nuria Fagella ; with contributions by Xavier Buff ... [et al.].
Author:	Branner, Bodil.
other author:	Fagella, Nuria.
Published:	Cambridge :Cambridge University Press, : 2014.,
Description:	xvii, 413 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
[NT 15003449]:	Machine generated contents note: 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. Hai;ssinsky; Bibliography; Symbol index; Index.
Subject:	Holomorphic mappings. -
Online resource:	https://doi.org/10.1017/CBO9781107337602
ISBN:	9781107337602

Quasiconformal surgery in holomorphic dynamics
Branner, Bodil.

Quasiconformal surgery in holomorphic dynamics[electronic resource] /Bodil Branner and Nuria Fagella ; with contributions by Xavier Buff ... [et al.]. - Cambridge :Cambridge University Press,2014. - xvii, 413 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;141. - Cambridge studies in advanced mathematics ;141..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Machine generated contents note: 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. Hai;ssinsky; Bibliography; Symbol index; Index.

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.

ISBN: 9781107337602Subjects--Topical Terms:

699810
Holomorphic mappings.

LC Class. No.: QA614.8 / .B725 2014

Dewey Class. No.: 515.98

Quasiconformal surgery in holomorphic dynamics
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100 1 $a Branner, Bodil. $3 698998
245 1 0 $a Quasiconformal surgery in holomorphic dynamics $h [electronic resource] / $c Bodil Branner and Nuria Fagella ; with contributions by Xavier Buff ... [et al.].
260 $a Cambridge : $b Cambridge University Press, $c 2014.
300 $a xvii, 413 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge studies in advanced mathematics ; $v 141
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 8 $a Machine generated contents note: 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. Hai;ssinsky; Bibliography; Symbol index; Index.
520 $a 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.
650 0 $a Holomorphic mappings. $3 699810
650 0 $a Differentiable dynamical systems. $3 524351
650 0 $a Kleinian groups. $3 706115
650 0 $a Global analysis (Mathematics) $3 631732
700 1 $a Fagella, Nuria. $3 3470538
830 0 $a Cambridge studies in advanced mathematics ; $v 141. $3 3470539
856 4 0 $u https://doi.org/10.1017/CBO9781107337602