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Fractals in Graz 2001

Analysis — Dynamics — Geometry — Stochastics

  • Conference proceedings
  • © 2003

Overview

Editors:
  1. Peter Grabner

    1. Institut für Mathematik A, Technische Universität Graz, Graz, Austria

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  2. Wolfgang Woess

    1. Institut für Mathematik C, Technische Universität Graz, Graz, Austria

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Part of the book series: Trends in Mathematics (TM)

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Table of contents (12 papers)

  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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Keywords

About this book

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.

Editors and Affiliations

  • 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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