Gaussian Self-Affinity and Fractals: Globality, the Earth, 1/F Noise, and R/S

ISBN-13: 9780387989938 / Angielski / Twarda / 2001 / 654 str.

Benoit B. Mandelbrot

Opis

Benoit Mandelbrot s pioneering research in fractal geometry has affected many areas of mathematics, physics, finance and other disciplines. The papers reprinted in this third volume of his Selected Works center on a detailed study of fractional Brownian functions, best known as the mathematical tools behind the celebrated fractal landscapes. Extensive introductory material preceding the reprints incorporates striking new observations and conjectures. This book explores the fractal themes of self-affinity and globality. The ubiquity of wild temporal and spatial variability led Mandelbrot, in the early 1960 s, to conclude that those phenomena lie beyond the usual statistical techniques and represent a new state of indeterminism. New mathematical tools are needed, and this book contributes to their development."

Recenzje

From the reviews of the first edition:

"Written in Mandelbrot's unique, thought-provoking style, these papers and commentaries contain a wealth of ideas which will appeal to mathematicians, statisticians, scientists and economists alike. It is a book both for dipping into and for detailed study, making readily accessible seminal papers which contain ideas that are as relevant now as when first published." (K. Falconer, Proceedings of the Edinburgh Mathematical Society, Vol. 48, 2005)

"This book contains the author's works in areas ranging from statistics, mathematics, physics, hydrology to economics and finance ... as well as more than 200 pages of new material written especially for this volume. ... To summarize, Volume H of Mandelbrot's Selecta is a major contribution to the understanding of wild self-affine variability and randomness. I believe that ... it will have a great impact on future research in mathematics, statistics, physics and other applied areas." (Yimin Xiao, Zentralblatt MATH, Vol. 1007, 2003)

"This book is a complete and encyclopaedic synthesis of problems and themes in self-affinity, fractals, multifractal geometry and globality. ... a very exhaustive and complete bibliography on the different connected subjects (with more than 500 references) may be very useful for researchers or users." (Michèle Mastrangelo-Dehen, Mathematical Reviews, Issue 2003 a)

"This volume is volume H of a program of publications of selected works (old and new) of Benoit B. Mandelbrot. ... The most valuable feature of the book is to bring together highly important papers ... for this reason this book should be in the library of any scientist interested in the origin of the concepts of self-affinity and fractals and their numerous applications in science." (Christian Michaux, Simon Stevin Bulletin, 2003)

Spis treści

Advances in Old But Open Topics * Broad Continuing Issues * Introductions from the 1960s * Fractional Brownian Motions * Fractional Brownian Surfaces * Self-Affine Cartoons in Grids; Their Multiple Fractal Dimensions * R/S Analysis and Its Uses

O autorze

Benoit B. Mandelbrot, geb. 1924 in Warschau, arbeitete als Mathematiker lange Zeit bei IBM, ist Honorarprofessor an der Yale University und Erfinder der fraktalen Geometrie. Mandelbrot lebt in Scarsdale, New York.