Invariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set / Edition 1

Invariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set / Edition 1

by Karsten Keller, K. Keller
     
 

ISBN-10: 3540674349

ISBN-13: 9783540674344

Pub. Date: 06/08/2000

Publisher: Springer Berlin Heidelberg

This book is mainly devoted to the combinatorics of quadratic holomorp hic dynamics. The conceptual kernel is a self-contained abstract count erpart of connected quadratic Julia sets which is built on Thurston's concept of a quadratic invariant lamination and on symbolic descriptio ns of the angle-doubling map. The theory obtained is illustrated in th e complex

Overview

This book is mainly devoted to the combinatorics of quadratic holomorp hic dynamics. The conceptual kernel is a self-contained abstract count erpart of connected quadratic Julia sets which is built on Thurston's concept of a quadratic invariant lamination and on symbolic descriptio ns of the angle-doubling map. The theory obtained is illustrated in th e 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 varia ble is assumed.

Product Details

ISBN-13:
9783540674344
Publisher:
Springer Berlin Heidelberg
Publication date:
06/08/2000
Series:
Lecture Notes in Mathematics Series , #1732
Edition description:
2000
Pages:
208
Product dimensions:
6.08(w) x 9.26(h) x 0.32(d)

Table of Contents

Abstract Julia sets.- The Abstract Mandelbrot set.- Abstract and concrete theory.

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