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Mathematics of fractals

Author: Masaya Yamaguchi; Masayoshi Hata; Jun Kigami
Publisher: Providence, R.I. : American Mathematical Society, ©1997.
Series: Translations of mathematical monographs, v. 167.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Explains the notions behind the self-similar sets called 'fractals' and 'chaotic dynamical systems'. This book emphasizes on the beautiful relationship between fractal functions (such as  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Masaya Yamaguchi; Masayoshi Hata; Jun Kigami
ISBN: 0821805371 9780821805374
OCLC Number: 36589536
Description: xi, 78 pages : illustrations ; 26 cm.
Contents: Ch. 1. The Fundamentals of Fractals. 1.1. What is the dimension? 1.2. Hausdorff measure and Hausdorff dimension. 1.3. Examples of fractals and their Hausdorff dimensions. 1.4. Nowhere-differentiable functions --
Ch. 2. Self-Similar Sets. 2.1. Existence and uniqueness. 2.2. The size and shape of a self-similar set. 2:3. Self-affine sets. 2:4. Fractals and chaos --
Ch. 3. An Alternative Computation for Differentiation. 3.1. A chaotic dynamical system and its generating function. 3.2. The Schauder expansion. 3.3. The de Rham equations and Lebesgue's singular function. 3.4. The system of difference equations of Lebesgue's function. 3.5. The relation between T(x) and M[subscript alpha](x) and its generalization. 3.6. Wavelet expansions --
Ch. 4. In Quest of Fractal Analysis. 4.1. The Sierpinski gasket. 4.2. The wave equation on the Sierpinski gasket. A physical observation. 4.3. The Laplacian on the Sierpinski gasket and a Gauss-Green type theorem.
Series Title: Translations of mathematical monographs, v. 167.
Other Titles: Furakutaru no sūri.
Responsibility: Masaya Yamaguti, Masayoshi Hata, Jun Kigami ; translated by Kiki Hudson.
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