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.
FREE Two-Day Shipping for Students. Learn more |
Book Description
Special Offers and Product Promotions
- Buy $50 in qualifying physical textbooks, get $5 in Amazon MP3 Credit. Here's how (restrictions apply)
Editorial Reviews
Review
Pleasant reading ... encourages the reader who is interested in fractals and their properties to pursue the study of the subject. -- Mathematical Reviews
This book is a good introduction to the topic. Interesting applications are presented. -- European Mathematical Society Newsletter
This book is a good introduction to the topic. Interesting applications are presented. -- European Mathematical Society Newsletter
Language Notes
Text: English (translation)
Original Language: Japanese
Original Language: Japanese
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
|
Share your thoughts with other customers:
|
||||||||||||||||||||||
|
Most Helpful Customer Reviews
4 of 4 people found the following review helpful:
5.0 out of 5 stars
To teach the subject.,
By Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - See all my reviews (VINE VOICE) (REAL NAME)
This review is from: Mathematics of Fractals (Translations of Mathematical Monographs) (Hardcover)
Sure, there are lots of pretty books on fractals!-- Colorful pictures, and all that! But 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 shows the student how to easily construct continuous, nowhere differentiable, functions;--it has great exercises, and it gives the student, and the readers, an appreciation of some of the deeper parts of the theory of chaotic dynamical systems.
Share your thoughts with other customers: Create your own review
|
|
Inside This Book
(learn more)
First Sentence:
In the long history of mathematics, we have seen a handful of peculiar sets and functions, well beyond ordinary imagination, that strongly impacted the mathematical environments of their times. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
open set condition, similar contractions, similarity dimension, outer measure, complete orthonormal basis, singular function, discrete dynamical system, topological dimension New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In the long history of mathematics, we have seen a handful of peculiar sets and functions, well beyond ordinary imagination, that strongly impacted the mathematical environments of their times. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
open set condition, similar contractions, similarity dimension, outer measure, complete orthonormal basis, singular function, discrete dynamical system, topological dimension New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 4
books:
5
books
cite this book:
- Collected Papers by Teiji Takagi on page 11
- The Geometry of Fractal Sets (Cambridge Tracts in Mathematics) by K. J. Falconer in Back Matter
- Dimension Theory (Princeton Mathematical Ser.; Vol 4) by Witold Hurewicz on page 2
- Fractal Geometry and Stochastics (Progress in Probability) by Christoph Bandt in Back Matter
- Computational Intelligence In Software Quality Assurance (Series in Machine Perception & Artifical Intelligence) (Series in Machine Perception and Artifical Intelligence) by S. Dick in Back Matter
- Exploring Chaos: Theory and Experiment by Brian Davies in Back Matter
- Exploring Chaos: Theory And Experiment (Studies in Nonlinearity) by Brian Davies in Back Matter
- Wavelet Analysis and Multiresolution Methods (Lecture Notes in Pure and Applied Mathematics) by Tian-Xiao He on page 366
- Analysis on Fractals (Cambridge Tracts in Mathematics) by Jun Kigami in Back Matter
Books on Related Topics
(learn more)
|
What Other Items Do Customers Buy After Viewing This Item?
Tags Customers Associate with This Product(What's this?)Click on a tag to find related items, discussions, and people.
|
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
