Braverman / Yampolsky Computability of Julia Sets

1. Auflage 2009
ISBN: 978-3-540-68547-0
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 151 Seiten

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, . 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.

Autoren/Hrsg.

Braverman, Mark

Yampolsky, Michael

Inhaltsverzeichnis

1;Contents;9
2;List of Notation;11
3;Introduction to Computability;12
4;Dynamics of Rational Mappings;31
5;First Examples;47
6;Positive Results;74
7;Negative Results;89
8;Computability versus Topological Propertiesof Julia Sets;127
9;Concluding Remarks;149
10;A Brief Historical Note;152
11;Index;156