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Catalogue Information
Field name	Details
Dewey Class	518.1
Title	Computability of Julia Sets (EB) / by Mark Braverman, Michael Yampolsky.
Author	Braverman, Mark
Added Personal Name	Yampolsky, Michael
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 2009.
Physical Details	: online resource.
Series	Algorithms and computation in mathematics 1431-1550 ; ; 23
ISBN	9783540685470
Summary Note	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.:
Contents note	1 Introduction to Computability -- 2 Dynamics of Rational Mappings -- 3 First Examples -- 4 Positive Results -- 5 Negative Results -- 6 Computability vs Topology -- References -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-540-68547-0
Links to Related Works	Subject References: Algebra . Algorithm Analysis and Problem Complexity . Algorithms . Mathematics . Mathematics of Computing . Theory of Computation . Authors: author . Braverman, Mark . Yampolsky, Michael . Corporate Authors: SpringerLink (Online service) . Series: Algorithms and computation in mathematics . Classification: 518.1 .

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Computability of Julia Sets

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