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Mathematics of Fractals
 
Edited by: Kiki Hudson
Masaya Yamaguti Ryukoku University, Ohtsu, Japan
Masayoshi Hata Kyoto University, Kyoto, Japan
Jun Kigami Kyoto University, Kyoto, Japan
Mathematics of Fractals
Hardcover ISBN:  978-0-8218-0537-4
Product Code:  MMONO/167
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4582-9
Product Code:  MMONO/167.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-0537-4
eBook: ISBN:  978-1-4704-4582-9
Product Code:  MMONO/167.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
Mathematics of Fractals
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Mathematics of Fractals
Edited by: Kiki Hudson
Masaya Yamaguti Ryukoku University, Ohtsu, Japan
Masayoshi Hata Kyoto University, Kyoto, Japan
Jun Kigami Kyoto University, Kyoto, Japan
Hardcover ISBN:  978-0-8218-0537-4
Product Code:  MMONO/167
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4582-9
Product Code:  MMONO/167.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-0537-4
eBook ISBN:  978-1-4704-4582-9
Product Code:  MMONO/167.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 1671997; 78 pp
    MSC: Primary 58; Secondary 70

    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.

  • Table of Contents
     
     
    • Chapters
    • The fundamentals of fractals
    • Self-similar sets
    • An alternative computation for differentiation
    • In quest of fractal analysis
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1671997; 78 pp
MSC: Primary 58; Secondary 70

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.

  • Chapters
  • The fundamentals of fractals
  • Self-similar sets
  • An alternative computation for differentiation
  • In quest of fractal analysis
  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.