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

ISBN-13: 9783764370060 / Angielski / Twarda / 2002 / 284 str.

Peter Grabner; Wolfgang Woess

Opis

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.

Spis treści

The Spectrum of the Laplacian on the Pentagasket.- From Fractal Groups to Fractal Sets.- Pointwise Estimates for Transition Probabilities of Random Walks on Infinite Graphs.- Piecewise Isometries — An Emerging Area of Dynamical Systems.- Random Walks on Sierpi?ski Graphs: Hyperbolicity and Stochastic Homogenization.- Some Remarks for Stable-like Jump Processes on Fractals.- Fractals, Multifunctions and Markov Operators.- Infinite Chains of Springs and Masses.- Self-similar Fractals and Self-similar Energies.- Neighbours of Self-affine Tiles in Lattice Tilings.- On the Hausdorff Dimension of the Sierpi?ski Gasket with respect to the Harmonic Metric.- Riesz Potentials and Besov Spaces on Fractals.- List of Participants.