Fractal Geometry and Stochastics II

2000
ISBN: 978-3-7643-6215-7
Verlag: Springer

Buch, Englisch, Band 46, 292 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1350 g

Reihe: Progress in Probability

The second conference on Fractal Geometry and Stochastics was held at Greifs­ wald/Koserow, Germany from August 28 to September 2, 1998. Four years had passed after the first conference with this theme and during this period the interest in the subject had rapidly increased. More than one hundred mathematicians from twenty-two countries attended the second conference and most of them presented their newest results. Since it is impossible to collect all these contributions in a book of moderate size we decided to ask the 13 main speakers to write an account of their subject of interest. The corresponding articles are gathered in this volume. Many of them combine a sketch of the historical development with a thorough discussion of the most recent results of the fields considered. We believe that these surveys are of benefit to the readers who want to be introduced to the subject as well as to the specialists. We also think that this book reflects the main directions of research in this thriving area of mathematics. We express our gratitude to the Deutsche Forschungsgemeinschaft whose financial support enabled us to organize the conference. The Editors Introduction Fractal geometry deals with geometric objects that show a high degree of irregu­ larity on all levels of magnitude and, therefore, cannot be investigated by methods of classical geometry but, nevertheless, are interesting models for phenomena in physics, chemistry, biology, astronomy and other sciences.

Zielgruppe

Research

Autoren/Hrsg.

Bandt, Christoph

Graf, Siegfried

Zähle, Martina

Fachgebiete

• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Naturwissenschaften Physik Physik Allgemein Geschichte der Physik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Bioinformatik
• Mathematik | Informatik EDV | Informatik Informatik
• Naturwissenschaften Biowissenschaften Angewandte Biologie Bioinformatik
• Mathematik | Informatik Mathematik Stochastik Elementare Stochastik
• Naturwissenschaften Physik Physik Allgemein Experimentalphysik
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Mathematik | Informatik Mathematik Geometrie Euklidische Geometrie
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Biowissenschaften Biowissenschaften
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Naturwissenschaften Chemie Chemie Allgemein Chemometrik, Chemoinformatik
• Naturwissenschaften Physik Quantenphysik

Inhaltsverzeichnis

1. Fractal Sets and Measures.- Multifractal Geometry.- Sixty Years of Bernoulli Convolutions.- 2. Iterated Function Systems.- Problems on Self-similar Geometry.- Problems on Self-similar Sets and Self-afHne Sets: An Update.- 3. Stochastic Processes, Random Fractals.- Selfsimilar Fractals and Selfsimilar Random Fractals.- Random Coverings and Multiplicative Processes.- Recent Results on Mandelbrot Multiplicative Cascades.- The Weierstrass-Mandelbrot Process Provides a Series Approximation to the Harmonizable Fractional Stable Motion.- 4. Fractals and Dynamical Systems.- An Ergodic Theoretic Approach to Mean Field Coupled Maps.- Entropy and Dimension Families Associated with Equilibrium Measures for Hyperbolic Dynamical Systems.- 5. Harmonic Analysis on Fractals.- On Limit Theorems for Brownian Motions on Unbounded Fractal Sets.- Heat Kernels and Spectral Asymptotics for some Random Sierpinski Gaskets.- Lagrangian Metrics and Fractal Dynamics.- List of Participants.