Computability of Julia Sets

Name: Computability of Julia Sets
SKU: 2705593
Price: 162.00 NZD
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Hardback

Series:

Algorithms and Computation in Mathematics

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Description

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.

Author Biography:

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

Release date NZ

November 26th, 2008

Author

Audiences

Postgraduate, Research & Scholarly
Professional & Vocational

Illustrations

XIII, 151 p.

Pages

151

Series

Algorithms and Computation in Mathematics

Dimensions

155x235x11

ISBN-13

9783540685463

Product ID

2705593

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