Computability of Julia Sets [electronic resource] /by Mark Braverman, Michael Yampolsky.
by Braverman, Mark [author.]; Yampolsky, Michael [author.]; SpringerLink (Online service).
Material type:
BookSeries: Algorithms and Computation in Mathematics: 23Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.Description: online resource.ISBN: 9783540685470.Subject(s): Mathematics | Information theory | Computer software | Computer science | Algebra | Algorithms | Mathematics | Algorithms | Theory of Computation | Algorithm Analysis and Problem Complexity | Mathematics of Computing | AlgebraDDC classification: 518.1 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
| MAIN LIBRARY | QA76.9.A43 (Browse shelf) | Available |
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| QA76.9.A43 Frontiers of High Performance Computing and Networking – ISPA 2006 Workshops | QA76.9.A43 Parallel and Distributed Processing and Applications | QA76.9.A43 Advances in Grid and Pervasive Computing | QA76.9.A43 Computability of Julia Sets | QA76.9.A43 Experimental Algorithms | QA76.9.A43 Algorithmic Aspects in Information and Management | QA76.9.A43 Combinatorial Pattern Matching |
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.
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