Computability of Julia Sets: 23 (Algorithms and Computation in Mathematics, 23) - Tapa dura

Libro 17 de 24: Algorithms and Computation in Mathematics

Braverman, Mark; Yampolsky, Michael

 
9783540685463: Computability of Julia Sets: 23 (Algorithms and Computation in Mathematics, 23)
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ISBN 10: 3540685464 ISBN 13: 9783540685463
Editorial: Springer, 2008

Sinopsis

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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Acerca del autor

M. Braverman is an expert in Theoretical Computer Science, particularly in applications of computability to Complex Analysis and Dynamical Systems M. Yampolsky is an expert in Dynamical Systems, particularly in Holomorphic Dynamics and Renormalization Theory

De la contraportada

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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Editorial
Springer
Año de publicación
2008
Idioma
Inglés
ISBN 10 
3540685464
ISBN 13 
9783540685463
Encuadernación
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Número de páginas
168
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Otras ediciones populares con el mismo título

9783642088063: Computability of Julia Sets: Algorithms and Computation in Mathematics: 23

Edición Destacada

ISBN 10:  3642088066 ISBN 13:  9783642088063
Editorial: Springer, 2010
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