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Fractal Geometry and Stochastics II

  • Conference proceedings
  • © 2000

Overview

Editors:
  1. Christoph Bandt

    1. Institut für Mathematik und Informatik, Ernst-Moritz-Arndt-Universität, Greifswald, Germany

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  2. Siegfried Graf

    1. Fakultät für Mathematik und Informatik, Universität Passau, Passau, Germany

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  3. Martina Zähle

    1. Mathematisches Institut, Friedrich-Schiller-Universität, Jena, Germany

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Part of the book series: Progress in Probability (PRPR, volume 46)

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Table of contents (13 papers)

  1. Front Matter

    Pages i-x
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  2. Fractal Sets and Measures

    1. Front Matter

      Pages 1-1
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    2. Multifractal Geometry

      • L. Olsen
      Pages 3-37

    3. Sixty Years of Bernoulli Convolutions

      • Yuval Peres, Wilhelm Schlag, Boris Solomyak
      Pages 39-65

  3. Iterated Function Systems

    1. Front Matter

      Pages 67-67
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    2. Problems on Self-similar Geometry

      • Manuel Moran
      Pages 69-93

    3. Problems on Self-similar Sets and Self-affine Sets: An Update

      • Yuval Peres, Boris Solomyak
      Pages 95-106

  4. Stochastic Processes and Random Fractals

    1. Front Matter

      Pages 107-107
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    2. Selfsimilar Fractals and Selfsimilar Random Fractals

      • John E. Hutchinson, Ludger Rüschendorf
      Pages 109-123

    3. Random Coverings and Multiplicative Processes

      • Jean-Pierre Kahane
      Pages 125-146

    4. Recent Results on Mandelbrot Multiplicative Cascades

      • Jacques Peyrière
      Pages 147-159

    5. The Weierstrass-Mandelbrot Process Provides a Series Approximation to the Harmonizable Fractional Stable Motion

      • Vladas Pipiras, Murad S. Taqqu
      Pages 161-179

  5. Fractals and Dynamical Systems

    1. Front Matter

      Pages 181-181
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    2. An Ergodic Theoretic Approach to Mean Field Coupled Maps

      • Gerhard Keller
      Pages 183-208

    3. Entropy and Dimension Families Associated with Equilibrium Measures for Hyperbolic Dynamical Systems

      • Yakov B. Pesin
      Pages 209-223

  6. Harmonic Analysis on Fractals

    1. Front Matter

      Pages 225-225
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    2. On Limit Theorems for Brownian Motions on Unbounded Fractal Sets

      • Masatoshi Fukushima
      Pages 227-237

    3. Heat Kernels and Spectral Asymptotics for some Random Sierpinski Gaskets

      • B. M. Hambly
      Pages 239-267

    4. Lagrangian Metrics and Fractal Dynamics

      • Umberto Mosco
      Pages 269-283

  7. Back Matter

    Pages 285-292
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Keywords

About this book

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.

Editors and Affiliations

  • Institut für Mathematik und Informatik, Ernst-Moritz-Arndt-Universität, Greifswald, Germany

    Christoph Bandt

  • Fakultät für Mathematik und Informatik, Universität Passau, Passau, Germany

    Siegfried Graf

  • Mathematisches Institut, Friedrich-Schiller-Universität, Jena, Germany

    Martina Zähle

Bibliographic Information

  • Book Title: Fractal Geometry and Stochastics II

  • Editors: Christoph Bandt, Siegfried Graf, Martina Zähle

  • Series Title: Progress in Probability

  • DOI: https://doi.org/10.1007/978-3-0348-8380-1

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag Basel 2000

  • Hardcover ISBN: 978-3-7643-6215-7Published: 14 February 2000

  • Softcover ISBN: 978-3-0348-9542-2Published: 23 October 2012

  • eBook ISBN: 978-3-0348-8380-1Published: 06 December 2012

  • Series ISSN: 1050-6977

  • Series E-ISSN: 2297-0428

  • Edition Number: 1

  • Number of Pages: X, 292

  • Topics: Probability Theory and Stochastic Processes, Mathematical Methods in Physics

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