Tale of Two Fractals

AvA.A. Kirillov

Häftad, Engelska, 2015

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Beskrivning

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

Produktinformation

Utgivningsdatum:2015-05-19
Mått:155 x 235 x 9 mm
Vikt:242 g
Format:Häftad
Språk:Engelska
Antal sidor:138
Upplaga:2013
Förlag:Springer-Verlag New York Inc.
ISBN:9781489997654

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Recensioner i media

From the reviews: "A Tale of Two Fractals was intended to bridge the gap between popular expositions on fractals and peer-reviewed research papers. ... Kirillov (Univ. of Pennsylvania) includes open questions and conjectures along with references to papers and books that expand upon particular topics beyond the scope of the present volume. ... the book is a useful addition to libraries supporting graduate programs in mathematics ... . Summing Up: Recommended. Graduate students and above." (C. Bauer, Choice, Vol. 51 (4), December, 2013) "This volume deals with several mathematical problems concerning the qualitative analysis of some models on fractal domains. The author is mainly concerned with the Sierpinski and Apollonian gaskets. ... This volume contains important advances in the theory of fractal sets or hyperbolic geometry. The book is a valuable resource for graduate students and researchers in applied nonlinear analysis." (Vicentiu D. Radulescu, zbMATH, Vol. 1273, 2013)

Innehållsförteckning

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.