Fractals in Graz 2001: Analysis, Dynamics, Geometry, StochasticsPeter J. Grabner, Wolfgang Woess 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. |
Contents
The Spectrum of the Laplacian on the Pentagasket | 1 |
From Fractal Groups to Fractal Sets | 25 |
Pointwise Estimates for Transition Probabilities of Random Walks on Infinite Graphs | 119 |
Piecewise Isometries An Emerging Area of Dynamical Systems | 135 |
Hyperbolicity and Stochastic Homogenization | 145 |
Some Remarks for Stablelike Jump Processes on Fractals | 185 |
Fractals Multifunctions and Markov Operators | 197 |
Infinite Chains of Springs and Masses | 211 |
Selfsimilar Fractals and Selfsimilar Energies | 225 |
Neighbours of Selfaffine Tiles in Lattice Tilings | 241 |
On the Hausdorff Dimension of the Sierpiriski Gasket with respect to the Harmonic Metric | 263 |
Riesz Potentials and Besov Spaces on Fractals | 271 |
List of Participants | 277 |
Other editions - View all
Fractals in Graz 2001: Analysis — Dynamics — Geometry — Stochastics Peter Grabner,Wolfgang Woess No preview available - 2012 |
Fractals in Graz 2001: Analysis — Dynamics — Geometry — Stochastics Peter J. Grabner,Wolfgang Woess No preview available - 2003 |
Common terms and phrases
algebra algorithm automaton automorphism Besov spaces Birkhäuser called compact construction corresponding defined Definition denote Dirichlet forms dynamical system edges eigenfunction eigenspaces eigenvalue equivalence relation Euclidean example exists extended Sierpiński Figure finitely presented fractal G(Zm geodesic graphs G(a Grigorchuk Grigorchuk group Gromov group G growth Hausdorff dimension homeomorphic hyperbolic group hyperbolic space implies infinite invariant inverse semigroup isometries isomorphic iterated function system iterated monodromy group Julia set kernel Lemma Let G limit space Markov chains Markov operator Math Mathematics metric space multifunction Neumann obtained Penrose tiling permutation Pn(x polynomial proof properties Proposition random walk representation respect Rostislav Schreier graphs Section self-affine self-similar self-similar action self-similar group self-similarity structure sequence Sierpiński gasket Sierpiński graph simple random walk spectrum subcycle subgroup subset symmetry Theorem topological transformations tree T(X triangles unique vertex vertices virtual endomorphism word