BeschreibungThe 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.
Inhaltsverzeichnis1. Fractal Sets and Measures.- Multifractal Geometry.- Sixty Years of Bernoulli Convolutions.- 2. Iterated Function Systems.- Problems on Self-similar Geometry.- Problems on Self-similar Sets and Self-afHne Sets: An Update.- 3. Stochastic Processes, Random Fractals.- Selfsimilar Fractals and Selfsimilar Random Fractals.- Random Coverings and Multiplicative Processes.- Recent Results on Mandelbrot Multiplicative Cascades.- The Weierstrass-Mandelbrot Process Provides a Series Approximation to the Harmonizable Fractional Stable Motion.- 4. Fractals and Dynamical Systems.- An Ergodic Theoretic Approach to Mean Field Coupled Maps.- Entropy and Dimension Families Associated with Equilibrium Measures for Hyperbolic Dynamical Systems.- 5. Harmonic Analysis on Fractals.- On Limit Theorems for Brownian Motions on Unbounded Fractal Sets.- Heat Kernels and Spectral Asymptotics for some Random Sierpinski Gaskets.- Lagrangian Metrics and Fractal Dynamics.- List of Participants.
Untertitel: 2000. Auflage. Book. Sprache: Englisch.
Erscheinungsdatum: Februar 2000
Seitenanzahl: 308 Seiten