Computability of Julia Sets

Name: Computability of Julia Sets
Brand: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
SKU: 9783540685463
Price: 59.31 EUR
Availability: InStock

Автор: Mark Braverman, Michael Yampolsky

Език:

Корици: С твърди корици

Издател: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Наличност: Външен склад в ограничено количество

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59.31 € 115.99 лв

Among all computer-generated mathematical images, Julia sets of rational maps occupy one of the most...

Информация за книгата

Автор

Mark Braverman, Michael Yampolsky

Език

Английски език

Корици

Книга - С твърди корици

Издадена

2008

страници

151

EAN

9783540685463

ISBN

3540685464

Enbook ID

02108072

Издател

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Теглоt

366

Размери

158 x 241 x 15

Пълно описание

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.

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