"Fractal Geometry and Stochastics I" by Kenneth J. Falconer, Christoph Bandt, Siegfried Graf, Martina Zähle

This volume is dedicated to Fractal geometry. The reader will be introduced to the most recent results in these subjects. Researchers and graduate students alike will benefit from the clear expositions.


Fractal geometry is a new and promising field for researchers from different disciplines such as mathematics, physics, chemistry, biology and medicine. It is used to model complicated natural and technical phenomena. The most convincing models contain an element of randomness so that the combination of fractal geometry and stochastics arises in between these two fields. It contains contributions by outstanding mathematicians and is meant to highlight the principal directions of research in the area. The contributors were the main speakers attending the conference "Fractal Geometry and Stochastics" held at Finsterbergen, Germany, in June 1994. This was the first international conference ever to be held on the topic.

The book is addressed to mathematicians and other scientists who are interested in the mathematical theory concerning:
• Fractal sets and measures
• Iterated function systems
• Random fractals
• Fractals and dynamical systems, and
• Harmonic analysis on fractals.
The reader will be introduced to the most recent results in these subjects. Researchers and graduate students alike will benefit from the clear expositions.


Contents
Probabilistic Methods in Fractal Geometry
Measures of Fractal Lacunarity: Minkowski Content and Alternatives
Tangent Measures, Densities, and Singular Integrals
Self-Similarity, L p -Spectrum and Multifractal Formalism
Infinite Iterated Function Systems: Theory and Applications.
Aspects of the Fractal Percolation Process
Fractals via Random Iterated Function Systems and Random Geometric Constructions
Remarks on Weak Limit Laws for Fractal Sets
A Rigidity Theorem in Complex Dynamics.
Estimates on the Spectrum of Fractals Arising from Affine Iterations
Laplacians on Self-Similar Sets and their Spectral Distributions