Falconer K. / Falconer K. - Fractal Geometry. Mathematical Foundations and Applications / Fractal geometry [1990, 2003, DjVu, ENG]

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Fractal Geometry. Mathematical Foundations and Applications / Фрактальная геометрия. Математические основы и приложения (1-е, 2-е издания)

Год: 1990, 2003
Автор: Falconer K. / Фальконер К.
Жанр: Учебное пособие
Издательство: John Wiley & Sons Ltd, England
ISBN: 0-471-92287-0, 0-470-84861-8, 0-470-84862-6
Язык: Английский
Формат: DjVu
Качество: Отсканированные страницы + слой распознанного текста
Количество страниц: 155 разворотов + 267

Описание: The main aim of the book is to provide a treatment of the mathematics associated with fractals and dimensions at a level which is reasonably accessible to those who encounter fractals in mathematics or science. Although basically a mathematics book, it attempts to provide an intuitive as well as a mathematical insight into the subject.
The book falls naturally into two parts. Part I is concerned with the general theory of fractals and thek geometry. Firstly, various notions of dimension and methods for thek calculation are introduced. Then geometrical properties of fractals are investigated in much the same way as one might study the geometry of classical figures such as circles or ellipses: locally a circle may be approximated by a line segment, the projection or 'shadow' of a circle is generally an ellipse, a ckcle typically intersects a straight line segment in two points (if at all), and so on. There are ffactal analogues of such properties, usually with dimension playing a key r61e. Thus we consider, for example, the local form of fractals, and projections and intersections of fractals.
Part II of the book contains examples of fractals, to which the theory of the first part may be applied, drawn from a wide variety of areas of mathematics and physics. Topics include 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.

Книга состоит из двух частей. Часть I посвящена общей теории фракталов. Часть II книги содержит примеры фракталов, взятые из самых разных областей математики и физики, в которых может быть применена теория из первой части.
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Издание 1990 года


Издание 2003 года


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