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978-3-540-68547-0
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20180115171702.0
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100301s2009 gw | s |||| 0|eng d
9783540685470
978-3-540-68547-0
10.1007/978-3-540-68547-0
doi
QA76.9.A43
PBKS
bicssc
COM051300
bisacsh
518.1
23
Braverman, Mark.
author.
Computability of Julia Sets
[electronic resource] /
by Mark Braverman, Michael Yampolsky.
Berlin, Heidelberg :
Springer Berlin Heidelberg,
2009.
XIII, 151 p.
online resource.
text
txt
rdacontent
computer
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rdamedia
online resource
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rda
Algorithms and Computation in Mathematics,
1431-1550 ;
23
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.
Mathematics.
Computer programming.
Computers.
Algorithms.
Computer science
Mathematics.
Algebra.
Mathematics.
Algorithms.
Algebra.
Programming Techniques.
Theory of Computation.
Algorithm Analysis and Problem Complexity.
Mathematics of Computing.
Yampolsky, Michael.
author.
SpringerLink (Online service)
Springer eBooks
Printed edition:
9783540685463
Algorithms and Computation in Mathematics,
1431-1550 ;
23
http://dx.doi.org/10.1007/978-3-540-68547-0
ZDB-2-SMA
372108
372108
0
0
0
0
EBook
elib
elib
2018-01-15
2018-01-15
2018-01-15
EBOOK