Braverman / Yampolsky Computability of Julia Sets

1. Auflage 2009
ISBN: 978-3-540-68547-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 23, 151 Seiten, eBook

Reihe: Algorithms and Computation in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Braverman, Mark

Yampolsky, Michael

Inhaltsverzeichnis

to Computability.- Dynamics of Rational Mappings.- First Examples.- Positive Results.- Negative Results.- Computability versus Topological Properties of Julia Sets.

Über Autor(innen)

M. Braverman is an expert in Theoretical Computer Science, particularly in applications of computability to Complex Analysis and Dynamical Systems

M. Yampolsky is an expert in Dynamical Systems, particularly in Holomorphic Dynamics and Renormalization Theory