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Mathematics of Fractals
Masaya Yamaguti, Ryukoku University, Ohtsu, Japan, and Masayoshi Hata and Jun Kigami, Kyoto University, Kyoto, Japan
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Translations of Mathematical Monographs
1997; 78 pp; hardcover
Volume: 167
ISBN-10: 0-8218-0537-1
ISBN-13: 978-0-8218-0537-4
List Price: US$47
Member Price: US$37.60
Order Code: MMONO/167
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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

"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

Table of Contents

  • The fundamentals of fractals
  • Self-similar sets
  • An alternative computation for differentiation
  • In quest of fractal analysis
  • Recommended reading
  • Index
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