Untertitel:: Algorithms and Computation in Mathematics
Verlag:: Springer Berlin
Erschienen:: 08.02.2009
Seitenanzahl:: 151
ISBN:: 3540685472
EAN:: 9783540685470
Format:: eBook
Schutz:: Dig. Wass.
Downloadzeit:: Maximaler Downloadzeitraum: 24 Monate

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Computability of Julia Sets

Mark Braverman / Michael Yampolsky

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 (most of it from the authors' own work) 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.