Fractal Geometry and Stochastics II

by Bandt, Christoph; Graf, Siegfried; Zahle, Martina

• ISBN13: 9783764362157
• ISBN10: 3764362154
• Format: Hardcover
• Copyright: 2000-04-01
• Publisher: Birkhauser

Summary

The combination of fractal geometry and stochastic methods can be used to create convincing models in many different areas of science such as biology, chemistry, computer science, mathematics and physics. The present book deals with the mathematical theory needed for this purpose. It contains contributions by outstanding mathematicians and is meant to highlight the principal directions of research in the field. The contributors were the main speakers at the conference Fractal Geometry and Stochastics II held at Greifswald/Koserow, Germany, in August 1998.The book is addressed to mathematicians and scientists who are interested in any of the following topics:· fractal dimensions· fractal measures and multifractals· self-similar and self-affine fractals· random fractals· stable processes· ergodic theory and dynamical systems· harmonic analysis and stochastic processes on fractalsThe readers will be introduced to the most recent results and problems on these subjects and also be treated to an overview of their historical development. Both researchers and graduate students will benefit from the clear expositions.

Table of Contents

Preface	vii
Introduction	ix
Fractal Sets and Measures	1	(66)
Multifractal Geometry	3	(36)
L. Olsen
Sixty Years of Bernoulli Convolutions	39	(28)
Yuval Peres
Wilhelm Schlag
Boris Solomyak
Iterated Function Systems	67	(40)
Problems on Self-similar Geometry	69	(26)
Manuel Moran
Problems on Self-similar Sets and Self-affine Sets: An Update	95	(12)
Yuval Peres
Boris Solomyak
Stochastic Processes, Random Fractals	107	(74)
Selfsimilar Fractals and Selfsimilar Random Fractals	109	(16)
John E. Hutchinson
Ludger Ruschendorf
Random Coverings and Multiplicative Processes	125	(22)
Jean-Pierre Kahane
Recent Results on Mandelbrot Multiplicative Cascades	147	(14)
Jacques Peyriere
The Weierstrass-Mandelbrot Process Provides a Series Approximation to the Harmonizable Fractional Stable Motion	161	(20)
Vladas Pipiras
Murad S. Taqqu
Fractals and Dynamical Systems	181	(44)
An Ergodic Theoretic Approach to Mean Field Coupled Maps	183	(26)
Gerhard Keller
Entropy and Dimension Families Associated with Equilibrium Measures for Hyperbolic Dynamical Systems	209	(16)
Yakov B. Pesin
Harmonic Analysis on Fractals	225	(60)
On Limit Theorems for Brownian Motions on Unbounded Fractal Sets	227	(12)
Masatoshi Fukushima
Heat Kernels and Spectral Asymptotics for some Random Sierpinski Gaskets	239	(30)
B.M. Hambly
Lagrangian Metrics and Fractal Dynamics	269	(16)
Umberto Mosco
List of Participants	285