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

  • Book
  • © 2000

Overview

Authors:
  1. Karsten Keller
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1732)

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction

    • Karsten Keller
    Pages 1-23

  3. Abstract Julia sets

    • Karsten Keller
    Pages 25-71

  4. The Abstract Mandelbrot set

    • Karsten Keller
    Pages 73-139

  5. Abstract and concrete theory

    • Karsten Keller
    Pages 141-180

  6. Back Matter

    Pages 181-206
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Invariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set

  • Authors: Karsten Keller

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0103999

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2000

  • Softcover ISBN: 978-3-540-67434-4Published: 06 May 2000

  • eBook ISBN: 978-3-540-45589-9Published: 06 May 2007

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 208

  • Topics: Partial Differential Equations, Topology

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