Quasiconformal Surgery in Holomorphic Dynamics - Bodil Branner, Núria Fagella

Quasiconformal Surgery in Holomorphic Dynamics

Buch | Hardcover
428 Seiten
2014
Cambridge University Press (Verlag)
978-1-107-04291-9 (ISBN)
109,70 inkl. MwSt
This comprehensive introduction is ideal for graduate students and researchers wishing to learn about quasiconformal surgery in holomorphic dynamics through a self-contained text. A wide variety of applications are included, and geometrical ideas are emphasised with plenty of illustrations that are seldom found in the literature at this level.
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.

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.

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.

Erscheint lt. Verlag 23.1.2014
Reihe/Serie Cambridge Studies in Advanced Mathematics
Zusatzinfo Worked examples or Exercises; 5 Halftones, unspecified; 105 Halftones, color; 25 Line drawings, unspecified
Verlagsort Cambridge
Sprache englisch
Maße 156 x 233 mm
Gewicht 850 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 1-107-04291-7 / 1107042917
ISBN-13 978-1-107-04291-9 / 9781107042919
Zustand Neuware
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