"Fractal Geometry and Stochastics III" by Andrzej Lasota, Józef Myjak, Martina Zähle, et al.

This book documents the establishment of fractal geometry as a substantial mathematical theory. Main topics include multifractal measures, dynamical systems, stochastic processes and random fractals, harmonic analysis on fractals.

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.

Contents
Preface
Markov Operators and Semifractals.
On Various Multifractal Spectra
One-Dimensional Moran Sets and the Spectrum of Schrödinger Operators
Small-scale Structure via Flows
Hausdorff Dimension of Hyperbolic Attractors in ℝ 3
The Exponent of Convergence of Kleinian Groups; on a Theorem of Bishop and Jones
Lyapunov Exponents Are not Rigid with Respect to Arithmetic Subsequences
Some Topics in the Theory of Multiplicative Chaos
Intersection Exponents and the Multifractal Spectrum for Measures on Brownian Paths
Additive Lévy Processes: Capacity and Hausdorff Dimension
The Fractal Laplacian and Multifractal Quantities
Geometric Representations of Currents and Distributions
Variational Principles and Transmission Conditions for Fractal Layers
Function Spaces and Stochastic Processes on Fractals
A Dirichlet Form on the Sierpinski Gasket, Related Function Spaces, and Traces
Spectral Zeta Function of Symmetric Fractals