A. A. Kirillov: A Tale of Two Fractals

Cover: 9781489997654 | A Tale of Two Fractals | A. A. Kirillov | Taschenbuch | xiii | 2015

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

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

Inhaltsverzeichnis

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

Details

Erscheinungsjahr:	2015
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xiii 138 S.
ISBN-13:	9781489997654
ISBN-10:	1489997652
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Kirillov, A. A.
Hersteller:	Springer New York Springer US, New York, N.Y.
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	235 x 155 x 9 mm
Von/Mit:	A. A. Kirillov
Erscheinungsdatum:	19.05.2015
Gewicht:	0,242 kg