Invariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set
This book is mainly devoted to the combinatorics of quadratic holomorphic dynamics. The conceptual kernel is a self-contained abstract counterpart of connected quadratic Julia sets which is built on Thurston's concept of a quadratic invariant lamination a
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Springer
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Karsten Keller
Invariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set
Springer
Author Karsten Keller Institute of Mathematics and Computer Science Ernst-Moritz-Arndt University Jahnstr. 15a 17487 Greifswald, Germany E-mail: [email protected]
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - ClP-Einheitsaufnahme Keller, Karsten: Invariant factors, Julia equivalences and the (abstract) Mandelbrot set! Karsten Keller. - Berlin; Heidelberg; New York; Barcelona; Hong Kong; London; Milan; Paris; Singapore; Tokyo: Springer, 2000 (Lecture notes in mathematics; 1732) ISBN 3-540-67434-9
Mathematics Subject Classification (2000): 30D05, 54H20, 37B 10 ISSN 0075-8434 ISBN 3-540-67434-9 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer- Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag is a company in the BertelsmannSpringer publishing group. © Springer-Verlag Berlin Heidelberg 2000 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the author Printed on acid-free paper SPIN: 10724999 41/3143/du
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To Anke, Dorthe, Svea and Wiete
Preface
This monograph is primarily concerned with the combinatorial structure of quadratic dynamics. It provides an enhanced and elaborated version of my habilitation thesis at Greifswald University, submitted at the end of 1995 and having its root in a series of papers in collaboration with my teacher and colleague Christoph Bandt. I want to thank first of all him for all his ideas and his immense share of work now hidden in this monograph. I also want to express my deep gratitude to Dierk Schleicher and Christopher Penrose for fruitful discussions and for sharing many of their ideas. Both have discussed the combinatorics of complex quadratic dynamics by using approaches similar to that presented here. I should thank Adrien Douady and John Hubbard for opening the interesting research field of quadratic dynamics and William P. Thurston for providing the basis of Chapters 2 and 3. Further, I want to underline that Chapter 4 has greatly benefited from the work of John Milnor and Dierk Schleicher. It is often not easy to trace bac
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