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＜電子ブック＞
Computability of Julia Sets / by Mark Braverman, Michael Yampolsky
(Algorithms and Computation in Mathematics ; 23)

版	1st ed. 2009.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2009
本文言語	英語
大きさ	XIII, 151 p : online resource
著者標目	*Braverman, Mark author Yampolsky, Michael author SpringerLink (Online service)
件　名	LCSH:Algorithms LCSH:Algebra LCSH:Computer programming LCSH:Computer science LCSH:Computer science -- Mathematics  全ての件名で検索 FREE:Algorithms FREE:Algebra FREE:Programming Techniques FREE:Theory of Computation FREE:Mathematics of Computing
一般注記	to Computability -- Dynamics of Rational Mappings -- First Examples -- Positive Results -- Negative Results -- Computability versus Topological Properties of Julia Sets 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 HTTP:URL=https://doi.org/10.1007/978-3-540-68547-0

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