Mathematics of fractals / Masaya Yamaguti, Masayoshi Hata, Jun Kigami ; translated by Kiki Hudson.

Por: Yamaguchi, Masaya, 1925-Colaborador(es): Hata, Masayoshi | Kigami, JunIdioma: Inglés Lenguaje original: Japonés Series Translations of mathematical monographs ; v. 167Editor: Providence, R.I. : American Mathematical Society, c1997Descripción: xi, 78 p. : ill. ; 26 cmISBN: 0821805371 (acidfree paper)Títulos uniformes: Furakutaru no sūri. English Tema(s): Fractals | Chaotic behavior in systemsOtra clasificación: *CODIGO*
Contenidos:
Contents --
Preface ix --
Preface to the English Translation xi --
Chapter 1. The Fundamentals of fractals [1] --
1.1. What is the dimension? [1] --
1.2. Hausdorff measure and Hausdorff dimension [4] --
1.3. Examples of fractals and their Hausdorff dimensions [7] --
1.4. Nowhere-differentiable functions [11] --
Exercises [14] --
Chapter 2. Self-Similar Sets [17] --
2.1. Existence and uniqueness [17] --
2.2. The size and shape of a self-similar set [20] --
2.3. Self-affine sets [26] --
2.4. fractals and chaos [29] --
Exercises [30] --
Chapter 3. An Alternative Computation for Differentiation [33] --
3.1. A chaotic dynamical system and its generating function [33] --
3.2. The Schauder expansion [36] --
3.3. The de Rham equations and Lebesgue’s singular function [38] --
3.4. The system of difference equations of Lebesgue’s function [41] --
3.5. The relation between T(x)and Ma(x) and its generalization [44] --
3.6. Wavelet expansions [47] --
Exercises [51] --
Chapter 4. In Quest of fractal Analysis [53] --
4.1. The Sierpinski gasket [53] --
4.2. The wave equation on the Sierpiiiski gasket. --
A physical observation [59] --
4.3. The Laplacian on the Sierpiinski gasket and a Gauss-Green type theorem [63] --
4.4. The Dirichlet problem for Poisson’s equation [68] --
Exercises [72] --
Recommended Reading [75] --
Index [77] --
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Includes bibliographical references (p. 75-76) and index.

Contents --
Preface ix --
Preface to the English Translation xi --
Chapter 1. The Fundamentals of fractals [1] --
1.1. What is the dimension? [1] --
1.2. Hausdorff measure and Hausdorff dimension [4] --
1.3. Examples of fractals and their Hausdorff dimensions [7] --
1.4. Nowhere-differentiable functions [11] --
Exercises [14] --
Chapter 2. Self-Similar Sets [17] --
2.1. Existence and uniqueness [17] --
2.2. The size and shape of a self-similar set [20] --
2.3. Self-affine sets [26] --
2.4. fractals and chaos [29] --
Exercises [30] --
Chapter 3. An Alternative Computation for Differentiation [33] --
3.1. A chaotic dynamical system and its generating function [33] --
3.2. The Schauder expansion [36] --
3.3. The de Rham equations and Lebesgue’s singular function [38] --
3.4. The system of difference equations of Lebesgue’s function [41] --
3.5. The relation between T(x)and Ma(x) and its generalization [44] --
3.6. Wavelet expansions [47] --
Exercises [51] --
Chapter 4. In Quest of fractal Analysis [53] --
4.1. The Sierpinski gasket [53] --
4.2. The wave equation on the Sierpiiiski gasket. --
A physical observation [59] --
4.3. The Laplacian on the Sierpiinski gasket and a Gauss-Green type theorem [63] --
4.4. The Dirichlet problem for Poisson’s equation [68] --
Exercises [72] --
Recommended Reading [75] --
Index [77] --

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