Fractal Geometry Stochastics

This book contains the proceedings of the conference "Fractals in Graz 2001 - Analysis, Dynamics, Geometry, Stochastics" that was held in the second week of June 2001 at Graz University of Technology, in the capital of Styria, southeastern province of Austria. The scientific committee of the meeting consisted of M. Barlow (Vancouver), R. Strichartz (Ithaca), P. Grabner and W. Woess (both Graz), the latter two being the local organizers and editors of this volume. We made an effort to unite in the conference as well as in the present pro­ ceedings a multitude of different directions of active current work, and to bring together researchers from various countries as well as research fields that all are linked in some way with the modern theory of fractal structures. Although (or because) in Graz there is only a very small group working on fractal structures, consisting of "non-insiders", we hope to have been successful with this program of wide horizons. All papers were written upon explicit invitation by the editors, and we are happy to be able to present this representative panorama of recent work on poten­ tial theory, random walks, spectral theory, fractal groups, dynamic systems, fractal geometry, and more. The papers presented here underwent a refereeing process.

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.

This volume is dedicated to Fractal geometry deals with geometric objects that show a high degree of irregu larity on all levels of magnitude and, therefore, cannot be investigated by methods of classical geometry but, nevertheless, are interesting models for phenomena in physics, chemistry, biology, astronomy and other sciences.

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.