Product Description
In mathematics the Mandelbrot set, named after Benoît Mandelbrot, is a set of points in the complex plane, the boundary of which forms a fractal. Mathematically the Mandelbrot set can be defined as the set of complex values of c for which the orbit of 0 under iteration of the complex quadratic polynomial zn+1 = zn2 + c remains bounded.[1] That is, a complex number, c, is in the Mandelbrot set if, when starting with z0=0 and applying the iteration repeatedly, the absolute value of zn never exceeds a certain number (that number depends on c) however large n gets. For example, letting c = 1 gives the sequence 0, 1, 2, 5, 26,?, which tends to infinity. As this sequence is unbounded, 1 is not an element of the Mandelbrot set. On the other hand, c = i (where i is the square root of -1) gives the sequence 0, i, (?1 + i), ?i, (?1 + i), ?i?, which is bounded and so i belongs to the Mandelbrot set. When computed and graphed on the complex plane the Mandelbrot Set is seen to have an elaborate boundary which does not simplify at any given magnification. ... Read more

Product Description
Certain noises, many aspects of turbulence, and almost all aspects of finance exhibit a level of temporal and spatial variability whose "wildness" impressed itself vividly upon the author, Benoit Mandelbrot, in the early 1960's. He soon realized that those phenomena cannot be described by simply adapting the statistical techniques of earlier physics, or even extending those techniques slightly. It appeared that the study of finance and turbulence could not move forward without the recognition that those phenomena represented a new second stage of indeterminism. Altogether new mathematical tools were needed. The papers in this Selecta volume reflect that realization and the work that Dr. Mandelbrot did toward the development of those new tools. ... Read more

Customer Reviews (2)

Clay
M. is a great man in (large) part because of what he has written, including these papers. And yes they are challenging. I find them nearly self-contained though.

No One Can Duplicate The Cover
I went and asked K. G. Monks for help. Even with his direction I only got a bad approximation.
The rest of the book is less readable than that. It is a collection of Dr. Mandelbrot's
old articles. I interviewed Dr. Mandelbrot several years ago before a lecture of his
at U. C. Riverside. He is not a very friendly or communicative man. His
articles in general are very hard to read and without adequate history and definitions.
It is , thus, incredible that his original book was such a success. Looking at
his work, I would call him a "noise" specialist and not a fractalist at all.
This book is really a book about very hard parts of noise theory.
In my mind Dr. Mandelbrot is very wrong in many of his conclusions ,
but he has some very nice results here. Don't
waste your money if you don't have a graduate degree in mathematics
with a specialization in noise, chaosand dynamics. Most of his recent
articles have been on multifractals applied to stockmarket theory.
He is one of the great men of our age
and these articles are his feet of clay. ... Read more

Product Description
This volume presents a systematic exposition of current knowledge about the Mandelbrot set and presents the latest research in complex dynamics. Topics discussed include the universality and the local connectivity of the Mandelbrot set, parabolic bifurcations, critical circle homeomorphisms, absolutely continuous invariant measures and matings of polynomials, along with the geometry, dimension and local connectivity of Julia sets. Chapters document important results hitherto unpublished or difficult to find in the literature. This book will be of interest to graduate students in mathematics, physics and mathematical biology, as well as to researchers in dynamical systems and Kleinian groups. ... Read more