Fractals in Graz 2001: Analysis — Dynamics — Geometry — Stochastics

Description

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. Front Matter....Pages i-vii Some Remarks for Stable-like Jump Processes on Fractals....Pages 185-196 Infinite Chains of Springs and Masses....Pages 211-223 The Spectrum of the Laplacian on the Pentagasket....Pages 1-24 Pointwise Estimates for Transition Probabilities of Random Walks on Infinite Graphs....Pages 119-134 Neighbours of Self-affine Tiles in Lattice Tilings....Pages 241-262 Riesz Potentials and Besov Spaces on Fractals....Pages 271-276 Fractals, Multifunctions and Markov Operators....Pages 197-210 Self-similar Fractals and Self-similar Energies....Pages 225-240 From Fractal Groups to Fractal Sets....Pages 25-118 Piecewise Isometries — An Emerging Area of Dynamical Systems....Pages 135-144 On the Hausdorff Dimension of the Sierpiński Gasket with respect to the Harmonic Metric....Pages 263-269 Random Walks on Sierpiński Graphs: Hyperbolicity and Stochastic Homogenization....Pages 145-183 Back Matter....Pages 277-284