**Translations of Mathematical Monographs**

1997;
78 pp;
Hardcover

MSC: Primary 58;
Secondary 70

**Print ISBN: 978-0-8218-0537-4
Product Code: MMONO/167**

List Price: $50.00

Individual Member Price: $40.00

# Mathematics of Fractals

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*Masaya Yamaguti; Masayoshi Hata; Jun Kigami*

This book aims at providing a handy explanation of the notions behind the self-similar sets called "fractals" and "chaotic dynamical systems". The authors emphasize the beautiful relationship between fractal functions (such as Weierstrass's) and chaotic dynamical systems; these nowhere-differentiable functions are generating functions of chaotic dynamical systems. These functions are shown to be in a sense unique solutions of certain boundary problems. The last chapter of the book treats harmonic functions on fractal sets.

#### Readership

Undergraduate students, graduate students, and research mathematicians interested in global analysis and analysis on manifolds.

#### Reviews & Endorsements

Pleasant reading … encourages the reader who is interested in fractals and their properties to pursue the study of the subject.

-- Mathematical Reviews

The book is a good introduction to the topic. Interesting applications are presented.

-- European Mathematical Society Newsletter

If you must pick a book, on which an instructor can base a course, then the material must be built up systematically — both making connections to fundamental and elementary ideas in analysis — and, at the same time, it must reach some high-points in the subject. This lovely little book does that … it has great exercises.

-- Palle Jorgensen