Fractals in Graz 2001

1. Front Matter

   Pages i-vii

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2. The Spectrum of the Laplacian on the Pentagasket

   • Bryant Adams, S. Alex Smith, Robert S. Strichartz, Alexander Teplyaev

   Pages 1-24

3. From Fractal Groups to Fractal Sets

   • Laurent Bartholdi, Rostislav Grigorchuk, Volodymyr Nekrashevych

   Pages 25-118

4. Pointwise Estimates for Transition Probabilities of Random Walks on Infinite Graphs

   • Thierry Coulhon, Alexander Grigor’yan

   Pages 119-134

5. Piecewise Isometries — An Emerging Area of Dynamical Systems

   • Arek Goetz

   Pages 135-144

6. Random Walks on Sierpiński Graphs: Hyperbolicity and Stochastic Homogenization

   • Vadim A. Kaimanovich

   Pages 145-183

7. Some Remarks for Stable-like Jump Processes on Fractals

   • Takashi Kumagai

   Pages 185-196

8. Fractals, Multifunctions and Markov Operators

   • Andrzej Lasota, Józef Myjak

   Pages 197-210

9. Infinite Chains of Springs and Masses

   • Michel Mendès France, Ahmed Sebbar

   Pages 211-223

10. Self-similar Fractals and Self-similar Energies

    • Volker Metz

    Pages 225-240

11. Neighbours of Self-affine Tiles in Lattice Tilings

    • Klaus Scheicher, Jörg M. Thuswaldner

    Pages 241-262

12. On the Hausdorff Dimension of the Sierpiński Gasket with respect to the Harmonic Metric

    • Elmar Teufl

    Pages 263-269

13. Riesz Potentials and Besov Spaces on Fractals

    • M. Zähle

    Pages 271-276

14. Back Matter

    Pages 277-284

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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.

• Area
• Dynamical systems
• Graph
• Random Walk
• Sim
• Stochastic processes
• Volume
• calculus
• discrete mathematics
• jump process
• probability theory
• similarity
• stochastic process

• Institut für Mathematik A, Technische Universität Graz, Graz, Austria

  Peter Grabner

• Institut für Mathematik C, Technische Universität Graz, Graz, Austria

  Wolfgang Woess

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