Fractal Geometry and Stochastics II

ISBN-13: 9783034895422 / Angielski / Miękka / 2012 / 292 str.

Christoph Bandt; Siegfried Graf; Martina Zahle

Opis

A collection of contributions by outstanding mathematicians, highlighting the principal directions of research on the combination of fractal geometry and stochastic methods. Clear expositions introduce the most recent results and problems on these subjects and give an overview of their historical development.

Spis treści

1. 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.