A Tale of Two Fractals

2013
ISBN: 978-1-4899-9765-4
Verlag: Springer

Buch, Englisch, 138 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 2409 g

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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Kirillov, A. A.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Geometrie der modernen Physik
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme

Inhaltsverzeichnis

Introduction.- Part 1. The Sierpinski Gasket.- Definition and General Properties.- The Laplace Operator on the Sierpinski Gasket.- Harmonic Functions on the Sierpinski 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.