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Fractal Geometry and Stochastics III

  • Conference proceedings
  • © 2004

Overview

Editors:
  1. Christoph Bandt

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

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  2. Umberto Mosco

    1. Department of Physics, University of Rome La Sapienza, Roma, Italy

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    You can also search for this editor in PubMed   Google Scholar

  3. Martina Zähle

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

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  • Written by top experts from all over the world
  • Surveys leading from an introduction to the edge of research
  • Develops tools for a deep understanding of fractals

Part of the book series: Progress in Probability (PRPR, volume 57)

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Table of contents (16 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. Markov Operators and Semifractals

      • Andrzej Lasota, Józef Myjak, Tomasz Szarek
      Pages 3-22

    3. On Various Multifractal Spectra

      • Jacques Lévy Véhel, Claude Tricot
      Pages 23-42

    4. One-Dimensional Moran Sets and the Spectrum of Schrödinger Operators

      • Zhi-Ying Wen
      Pages 43-56

  3. Fractals and Dynamical Systems

    1. Front Matter

      Pages 57-57
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    2. Small-scale Structure via Flows

      • Albert M. Fisher
      Pages 59-78

    3. Hausdorff Dimension of Hyperbolic Attractors in ℝ3

      • Károly Simon
      Pages 79-92

    4. The Exponent of Convergence of Kleinian Groups; on a Theorem of Bishop and Jones

      • Bernd O. Stratmann
      Pages 93-107

    5. Lyapunov Exponents Are not Rigid with Respect to Arithmetic Subsequences

      • Amiran Ambroladze, Jörg Schmeling
      Pages 109-116

  4. Stochastic Processes and Random Fractals

    1. Front Matter

      Pages 117-117
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    2. Some Topics in the Theory of Multiplicative Chaos

      • Ai Hua Fan
      Pages 119-134

    3. Intersection Exponents and the Multifractal Spectrum for Measures on Brownian Paths

      • Peter Mörters
      Pages 135-150

    4. Additive Lévy Processes: Capacity and Hausdorff Dimension

      • Davar Khoshnevisan, Yimin Xiao
      Pages 151-170

  5. Fractal Analysis in Euclidean Space

    1. Front Matter

      Pages 171-171
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    2. The Fractal Laplacian and Multifractal Quantities

      • Hans Triebel
      Pages 173-192

    3. Geometric Representations of Currents and Distributions

      • Jenny Harrison
      Pages 193-204

    4. Variational Principles and Transmission Conditions for Fractal Layers

      • Maria Agostina Vivaldi
      Pages 205-217

  6. Harmonic Analysis on Fractals

    1. Front Matter

      Pages 219-219
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    2. Function Spaces and Stochastic Processes on Fractals

      • Takashi Kumagai
      Pages 221-234
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Keywords

About this book

Fractal geometry is used to model complicated natural and technical phenomena in various disciplines like physics, biology, finance, and medicine. Since most convincing models contain an element of randomness, stochastics enters the area in a natural way. This book documents the establishment of fractal geometry as a substantial mathematical theory. As in the previous volumes, which appeared in 1998 and 2000, leading experts known for clear exposition were selected as authors. They survey their field of expertise, emphasizing recent developments and open problems. Main topics include multifractal measures, dynamical systems, stochastic processes and random fractals, harmonic analysis on fractals.

Editors and Affiliations

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

    Christoph Bandt

  • Department of Physics, University of Rome La Sapienza, Roma, Italy

    Umberto Mosco

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

    Martina Zähle

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