A Tale of Two Fractals

Written by the celebrated mathematician and educator A.A. Kirillov, this book offers an original treatment of fractals that is accessible to beginners and sufficiently rigorous for serious mathematicians. Offers a solid foundation in the theory 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.

First book to provide a rigorous study of fractals usable by undergraduates Written by a renowned authority in the field and expert at communicating mathematical ideas to students An excellent means for young mathematicians to acquire basic tools from many different areas Abundant figures and exercises provide valuable clarity and practice

Zusammenfassung
Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals.

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