TY - BOOK
AU - Braverman,Mark
AU - Yampolsky,Michael
ED - SpringerLink (Online service)
TI - Computability of Julia Sets
T2 - Algorithms and Computation in Mathematics,
SN - 9783540685470
AV - QA76.9.A43
U1 - 518.1 23
PY - 2009///
CY - Berlin, Heidelberg
PB - Springer Berlin Heidelberg
KW - Mathematics
KW - Computer programming
KW - Computers
KW - Algorithms
KW - Computer science
KW - Algebra
KW - Programming Techniques
KW - Theory of Computation
KW - Algorithm Analysis and Problem Complexity
KW - Mathematics of Computing
N1 - to Computability -- Dynamics of Rational Mappings -- First Examples -- Positive Results -- Negative Results -- Computability versus Topological Properties of Julia Sets
N2 - 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
UR - http://dx.doi.org/10.1007/978-3-540-68547-0
ER -