Computability of Julia Sets
Braverman, Mark.
creator
author.
Yampolsky, Michael.
author.
SpringerLink (Online service)
text
gw
2009
monographic
eng
access
XIII, 151 p. online resource.
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.
to Computability -- Dynamics of Rational Mappings -- First Examples -- Positive Results -- Negative Results -- Computability versus Topological Properties of Julia Sets.
by Mark Braverman, Michael Yampolsky.
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
QA76.9.A43
518.1
Springer eBooks
Algorithms and Computation in Mathematics, 23
9783540685470
http://dx.doi.org/10.1007/978-3-540-68547-0
http://dx.doi.org/10.1007/978-3-540-68547-0
100301
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