A Tale of Two Fractals
Seiten
2015
Springer-Verlag New York Inc.
978-1-4899-9765-4 (ISBN)
Springer-Verlag New York Inc.
978-1-4899-9765-4 (ISBN)
Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals.
Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is intended to help bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, non-specialist mathematicians a solid foundation in the theory of fractals, and, in the process, to equip them with exposure to a variety of geometric, analytical, and algebraic tools with applications across other areas.
Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is intended to help bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, non-specialist mathematicians a solid foundation in the theory of fractals, and, in the process, to equip them with exposure to a variety of geometric, analytical, and algebraic tools with applications across other areas.
Introduction.- Part 1. The Sierpiński Gasket.- Definition and General Properties.- The Laplace Operator on the Sierpiński Gasket.- Harmonic Functions on the Sierpiński Gasket.- Part 2. The Apollonian Gasket.- Introduction.- Circles and Disks on Spheres.- Definition of the Apollonian Gasket.- Arithmetic Properties of Apollonian Gaskets.- Geometric and Group-Theoretic Approach.- Many-Dimensional Apollonian Gaskets.- Bibliography.
| Zusatzinfo | XIII, 138 p. |
|---|---|
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Informatik ► Software Entwicklung ► User Interfaces (HCI) |
| Mathematik / Informatik ► Informatik ► Theorie / Studium | |
| Mathematik / Informatik ► Mathematik ► Algebra | |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Mathematik / Informatik ► Mathematik ► Graphentheorie | |
| ISBN-10 | 1-4899-9765-2 / 1489997652 |
| ISBN-13 | 978-1-4899-9765-4 / 9781489997654 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
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