Fractal Geometry and Stochastics III

✍ Scribed by Andrzej Lasota, Józef Myjak, Tomasz Szarek (auth.), Christoph Bandt, Umberto Mosco, Martina Zähle (eds.)

• Publisher: Birkhäuser Basel
• Year: 2004
• Tongue: English
• Leaves: 264
• Series: Progress in Probability 57
• Edition: 1
• Category: Library

✦ Synopsis

Fractal geometry is used to model complicated natural and technical phenomena in various disciplines like physics, biology, finance, and medicine. Since most convincing models contain an element of randomness, stochastics enters the area in a natural way. This book documents the establishment of fractal geometry as a substantial mathematical theory. As in the previous volumes, which appeared in 1998 and 2000, leading experts known for clear exposition were selected as authors. They survey their field of expertise, emphasizing recent developments and open problems. Main topics include multifractal measures, dynamical systems, stochastic processes and random fractals, harmonic analysis on fractals.

✦ Table of Contents

Front Matter....Pages i-x
Front Matter....Pages 1-1
Markov Operators and Semifractals....Pages 3-22
On Various Multifractal Spectra....Pages 23-42
One-Dimensional Moran Sets and the Spectrum of Schrödinger Operators....Pages 43-56
Front Matter....Pages 57-57
Small-scale Structure via Flows....Pages 59-78
Hausdorff Dimension of Hyperbolic Attractors in ℝ 3 ....Pages 79-92
The Exponent of Convergence of Kleinian Groups; on a Theorem of Bishop and Jones....Pages 93-107
Lyapunov Exponents Are not Rigid with Respect to Arithmetic Subsequences....Pages 109-116
Front Matter....Pages 117-117
Some Topics in the Theory of Multiplicative Chaos....Pages 119-134
Intersection Exponents and the Multifractal Spectrum for Measures on Brownian Paths....Pages 135-150
Additive Lévy Processes: Capacity and Hausdorff Dimension....Pages 151-170
Front Matter....Pages 171-171
The Fractal Laplacian and Multifractal Quantities....Pages 173-192
Geometric Representations of Currents and Distributions....Pages 193-204
Variational Principles and Transmission Conditions for Fractal Layers....Pages 205-217
Front Matter....Pages 219-219
Function Spaces and Stochastic Processes on Fractals....Pages 221-234
A Dirichlet Form on the Sierpinski Gasket, Related Function Spaces, and Traces....Pages 235-244
Spectral Zeta Function of Symmetric Fractals....Pages 245-262

✦ Subjects

Probability Theory and Stochastic Processes;Dynamical Systems and Ergodic Theory;Measure and Integration;Calculus of Variations and Optimal Control;Optimization;Mathematical Methods in Physics