Mandelbrot is a world renowned scientist, known for his pioneering research in fractal geometry and chaos theory. In this volume, Mandelbrot defends the view that multifractals are intimately interrelated through the two fractal themes of wildness and self-affinity . This link involves a powerful collection of technical tools, which are of use to diverse scientific communities. Among the topics covered are: 1/f noise, fractal dimension and turbulence, sporadic random functions, and a new model for error clustering on telephone circuits.
By:
Benoit B. Mandelbrot
Contributions by:
J.M. Berger,
J.-P. Kahane,
J. Peyriere
Imprint: Springer-Verlag New York Inc.
Country of Publication: United States
Edition: Softcover reprint of the original 1st ed. 1999
Dimensions:
Height: 235mm,
Width: 155mm,
Spine: 23mm
Weight: 694g
ISBN: 9781461274346
ISBN 10: 1461274346
Pages: 442
Publication Date: 03 January 2014
Audience:
Professional and scholarly
,
Undergraduate
Format: Paperback
Publisher's Status: Active
Preface.- Panorama of grid-bound self affine variablity.- Sketches of prehistory and history.- Scaling, invariants and fixed points.- Filtering and specifications of self-affinity.- Short pieces.- New model for error clustering on telephone circuits.- Additional tests on clustering.- Self-similarity and conditional stationarity.- 1/f noises and the infrared catastrophe.- Co-indicator functions and related 1/f noises.- Sporadic random functions and conditional spectra: Self-similar examples and limits.- Random sets of multiplicity for trigonometric series.- Sporadic turbulence.- Intermittent free turbulence.- Lognormal hypothesis and distribution of energy dissipation in intermittent turbulence.- Intermittent turbulence in self-similar cascades: Divergence of high moments and dimension of the carrier.- Iterated random multiplications and invariance under randomly weighted averaging.- 'On certain martingales of Benoit Mandelbrot'.- Intermittent turbulence and fractal dimension: the kurtosis and the spectral exponent 5 3 + B.- Fractal dimension, dispersion, and singularities of fluid motion.- Elementary fractals and multifractals.- Bibliography.- Index.
