Computability of Julia Sets / Edition 1

Computability of Julia Sets / Edition 1

by Mark Braverman, Michael Yampolsky
     
 

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ISBN-10: 3642088066

ISBN-13: 9783642088063

Pub. Date: 11/23/2010

Publisher: Springer Berlin Heidelberg

Among all computer-generated mathematical images, Julia sets of rational maps occupy one of the most prominent positions. Their beauty and complexity can be fascinating. They also hold a deep mathematical content.

Computational hardness of Julia sets is the main subject of this book. By definition, a computable set in the plane can be visualized on a computer

Overview

Among all computer-generated mathematical images, Julia sets of rational maps occupy one of the most prominent positions. Their beauty and complexity can be fascinating. They also hold a deep mathematical content.

Computational hardness of Julia sets is the main subject of this book. By definition, a computable set in the plane can be visualized on a computer screen with an arbitrarily high magnification. There are countless programs to draw Julia sets. Yet, as the authors have discovered, it is possible to constructively produce examples of quadratic polynomials, whose Julia sets are not computable. This result is striking - it says that while a dynamical system can be described numerically with an arbitrary precision, the picture of the dynamics cannot be visualized.

The book summarizes the present knowledge (most of it from the authors' own work) about the computational properties of Julia sets in a self-contained way. It is accessible to experts and students with interest in theoretical computer science or dynamical systems.

Product Details

ISBN-13:
9783642088063
Publisher:
Springer Berlin Heidelberg
Publication date:
11/23/2010
Series:
Algorithms and Computation in Mathematics Series , #23
Edition description:
Softcover reprint of hardcover 1st ed. 2009
Pages:
151
Product dimensions:
6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

1 Introduction to Computability.- 2 Dynamics of Rational Mappings.- 3 First Examples.- 4 Positive Results.- 5 Negative Results.- 6 Computability vs Topology.- References.- Index

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