ENGLISH

Computability of Julia Sets

By Mark Braverman , Michael Yampolsky (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2009
ISBN
3540685464, 9783540685463, 9783540685470, 3540685472
DOI
10.1007/978-3-540-68547-0
ISSN
1431-1550
Language
english
Format
PDF
Filesize
3 MB (3497584 bytes)
Series
Algorithms and Computation in Mathematics 23
Edition
1
Pages
151\158
Topic
Computers
Library
Kolxo3
Time added
2009-12-04 00:34:26
Algorithms; Theory of Computation; Algorithm Analy

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 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.

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