Invariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set

  • Authors
  • Karsten┬áKeller

Part of the Lecture Notes in Mathematics book series (LNM, volume 1732)

Table of contents

  1. Front Matter
    Pages I-X
  2. Karsten Keller
    Pages 1-23
  3. Karsten Keller
    Pages 25-71
  4. Karsten Keller
    Pages 73-139
  5. Karsten Keller
    Pages 141-180
  6. Back Matter
    Pages 181-206

About this book

Introduction

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 and on symbolic descriptions of the angle-doubling map. The theory obtained is illustrated in the complex plane. It is used to give rigorous proofs of some well-known and some partially new statements on the structure of the Mandelbrot set. The text is intended for graduate students and researchers. Some elementary knowledge in topology and in functions of one complex variable is assumed.

Keywords

Julia set Mandelbrot set Quadratic Iteraction set topology

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0103999
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-67434-4
  • Online ISBN 978-3-540-45589-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book