CiNii 図書 - Fractal geometry : mathematical foundations and applications

An accessible introduction to fractals, useful as a text or reference. Part I is concerned with the general theory of fractals and their geometry, covering dimensions and their methods of calculation, plus the local form of fractals and their projections and intersections. Part II contains examples of fractals drawn from a wide variety of areas of mathematics and physics, including self-similar and self-affine sets, graphs of functions, examples from number theory and pure mathematics, dynamical systems, Julia sets, random fractals and some physical applications. Also contains many diagrams and illustrative examples, includes computer drawings of fractals, and shows how to produce further drawings for themselves.

FOUNDATIONS. Mathematical Background. Hausdorff Measure and Dimension. Alternative Definitions of Dimension. Techniques for Calculating Dimensions. Local Structure of Fractals. Projections of Fractals. Products of Fractals. Intersections of Fractals. APPLICATIONS AND EXAMPLES. Fractals Defined by Transformations--Self-Similar and Self-Affine Sets. Examples from Number Theory. Graphs of Functions. Examples from Pure Mathematics. Dynamical Systems. Iteration of Complex Functions--Julia Sets. Random Fractals. Brownian Motion and Brownian Surfaces. Multifractal Measures. Physical Applications. References. Index.

巻冊次: : pbk ISBN 9780471967774

内容説明

This paperback edition of Fractal Geometry provides an accessible treatment of the mathematics of fractals and their dimensions. It is aimed at those wanting to use fractals in their own areas of mathematics or science. The first part of the book covers the general theory of fractals and their geometry. Results are stated precisely, but technical measure theoretic ideas are avoided and difficult proofs are sketched. The second part contains a wide variety of examples and applications in mathematics and physics. The book contains numerous diagrams and illustrative examples. Each chapter ends with self-study exercises and suggestions for further reading. The author provides an intuitive as well as a mathematical insight into the subject.

Part I Foundations: mathematical background
Hausdorff measure and dimension
alternative definitions of dimension
techniques for calculating dimensions
local structure of fractals
projections of fractals
products of fractals
intersections of fractals. Part II Applications and examples: fractals defined by transformations
examples from number theory
graphs of functions
examples from pure mathematics
dynamical systems
iteration of complex functions-Julia sets
random fractals
Brownian motion and Brownian surfaces
multifractal measures
physical applications.

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Fractal geometry : mathematical foundations and applications

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