Ebook: Fractals in Graz 2001: Analysis — Dynamics — 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.

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This book contains the proceedings of the conference "Fractals in Graz 2001 - Analysis, Dynamics, Geometry, Stochastics" that was held in June 2001 at Graz University of Technology, Styria, Austria. The volume presents a multitude of different directions of active current research linked with the modern theory of fractal structures. All papers were written upon invitation by the editors. The book is addressed to mathematicians and scientists who are interested in any of the following topics: - fractal dimensions - fractal energies - fractal groups - stochastic processes on fractals - self-similarity - spectra of random walks - tilings - analysis on fractals - dynamical systems. The readers will be introduced to the most recent results and problems on these subjects. Both researchers and graduate students will benefit from the clear expositions.

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This book contains the proceedings of the conference "Fractals in Graz 2001 - Analysis, Dynamics, Geometry, Stochastics" that was held in June 2001 at Graz University of Technology, Styria, Austria. The volume presents a multitude of different directions of active current research linked with the modern theory of fractal structures. All papers were written upon invitation by the editors. The book is addressed to mathematicians and scientists who are interested in any of the following topics: - fractal dimensions - fractal energies - fractal groups - stochastic processes on fractals - self-similarity - spectra of random walks - tilings - analysis on fractals - dynamical systems. The readers will be introduced to the most recent results and problems on these subjects. Both researchers and graduate students will benefit from the clear expositions.
Content:
Front Matter....Pages i-vii
The Spectrum of the Laplacian on the Pentagasket....Pages 1-24
Neighbours of Self-affine Tiles in Lattice Tilings....Pages 241-262
Random Walks on Sierpi?ski Graphs: Hyperbolicity and Stochastic Homogenization....Pages 145-183
Fractals, Multifunctions and Markov Operators....Pages 197-210
From Fractal Groups to Fractal Sets....Pages 25-118
Piecewise Isometries — An Emerging Area of Dynamical Systems....Pages 135-144
Some Remarks for Stable-like Jump Processes on Fractals....Pages 185-196
Infinite Chains of Springs and Masses....Pages 211-223
Pointwise Estimates for Transition Probabilities of Random Walks on Infinite Graphs....Pages 119-134
On the Hausdorff Dimension of the Sierpi?ski Gasket with respect to the Harmonic Metric....Pages 263-269
Riesz Potentials and Besov Spaces on Fractals....Pages 271-276
Self-similar Fractals and Self-similar Energies....Pages 225-240
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 June 2001 at Graz University of Technology, Styria, Austria. The volume presents a multitude of different directions of active current research linked with the modern theory of fractal structures. All papers were written upon invitation by the editors. The book is addressed to mathematicians and scientists who are interested in any of the following topics: - fractal dimensions - fractal energies - fractal groups - stochastic processes on fractals - self-similarity - spectra of random walks - tilings - analysis on fractals - dynamical systems. The readers will be introduced to the most recent results and problems on these subjects. Both researchers and graduate students will benefit from the clear expositions.
Content:
Front Matter....Pages i-vii
The Spectrum of the Laplacian on the Pentagasket....Pages 1-24
Neighbours of Self-affine Tiles in Lattice Tilings....Pages 241-262
Random Walks on Sierpi?ski Graphs: Hyperbolicity and Stochastic Homogenization....Pages 145-183
Fractals, Multifunctions and Markov Operators....Pages 197-210
From Fractal Groups to Fractal Sets....Pages 25-118
Piecewise Isometries — An Emerging Area of Dynamical Systems....Pages 135-144
Some Remarks for Stable-like Jump Processes on Fractals....Pages 185-196
Infinite Chains of Springs and Masses....Pages 211-223
Pointwise Estimates for Transition Probabilities of Random Walks on Infinite Graphs....Pages 119-134
On the Hausdorff Dimension of the Sierpi?ski Gasket with respect to the Harmonic Metric....Pages 263-269
Riesz Potentials and Besov Spaces on Fractals....Pages 271-276
Self-similar Fractals and Self-similar Energies....Pages 225-240
Back Matter....Pages 277-284
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