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Fractal Geometry and Stochastics V

  • Conference proceedings
  • © 2015

Overview

Editors:
  1. Christoph Bandt

    1. Institut für Mathematik und Informatik, Universität Greifswald, Greifswald, Germany

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  2. Kenneth Falconer

    1. Mathematical Institute, University of St Andrews, St Andrews, United Kingdom

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  3. Martina Zähle

    1. Institut für Mathematik, Friedrich-Schiller-Universität Jena, Jena, Germany

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Part of the book series: Progress in Probability (PRPR, volume 70)

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Table of contents (17 papers)

  1. Front Matter

    Pages i-x
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  2. Geometric Measure Theory

    1. Front Matter

      Pages 1-1
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    2. Sixty Years of Fractal Projections

      • Kenneth Falconer, Jonathan Fraser, Xiong Jin
      Pages 3-25

    3. Scenery Flow, Conical Densities, and Rectifiability

      • Antti Käenmäki
      Pages 27-38

    4. The Shape of Anisotropic Fractals: Scaling of Minkowski Functionals

      • Philipp Schönhöfer, Klaus Mecke
      Pages 39-52

    5. Projections of Self-Similar and Related Fractals: A Survey of Recent Developments

      • Pablo Shmerkin
      Pages 53-74

  3. Self-Similar Fractals and Recurrent Structures

    1. Front Matter

      Pages 75-75
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    2. Dimension of the Graphs of the Weierstrass-Type Functions

      • Krzysztof Barański
      Pages 77-91

    3. Tiling \(\mathbb{Z}^{2}\) by a Set of Four Elements

      • De-Jun Feng, Yang Wang
      Pages 93-103

    4. Some Recent Developments in Quantization of Fractal Measures

      • Marc Kesseböhmer, Sanguo Zhu
      Pages 105-120

    5. Apollonian Circle Packings

      • Mark Pollicott
      Pages 121-142

    6. Entropy of Lyapunov-Optimizing Measures of Some Matrix Cocycles

      • Michał Rams
      Pages 143-154

  4. Analysis and Algebra on Fractals

    1. Front Matter

      Pages 155-155
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    2. Poincaré Functional Equations, Harmonic Measures on Julia Sets, and Fractal Zeta Functions

      • Peter J. Grabner
      Pages 157-174

    3. From Self-Similar Groups to Self-Similar Sets and Spectra

      • Rostislav Grigorchuk, Volodymyr Nekrashevych, Zoran Šunić
      Pages 175-207

    4. Finite Energy Coordinates and Vector Analysis on Fractals

      • Michael Hinz, Alexander Teplyaev
      Pages 209-227

    5. Fractal Zeta Functions and Complex Dimensions: A General Higher-Dimensional Theory

      • Michel L. Lapidus, Goran Radunović, Darko Žubrinić
      Pages 229-257

  5. Multifractal Theory

    1. Front Matter

      Pages 259-259
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    2. Inverse Problems in Multifractal Analysis

      • Julien Barral
      Pages 261-278

    3. Multifractal Analysis Based on p-Exponents and Lacunarity Exponents

      • Patrice Abry, Stéphane Jaffard, Roberto Leonarduzzi, Clothilde Melot, Herwig Wendt
      Pages 279-313
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Keywords

About this book

This book collects significant contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five topical sections: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. Each part starts with a state-of-the-art survey followed by papers covering a specific aspect of the topic. The authors are leading world experts and present their topics comprehensibly and attractively. Both newcomers and specialists in the field will benefit from this book.

Editors and Affiliations

  • Institut für Mathematik und Informatik, Universität Greifswald, Greifswald, Germany

    Christoph Bandt

  • Mathematical Institute, University of St Andrews, St Andrews, United Kingdom

    Kenneth Falconer

  • Institut für Mathematik, Friedrich-Schiller-Universität Jena, Jena, Germany

    Martina Zähle

Bibliographic Information

  • Book Title: Fractal Geometry and Stochastics V

  • Editors: Christoph Bandt, Kenneth Falconer, Martina Zähle

  • Series Title: Progress in Probability

  • DOI: https://doi.org/10.1007/978-3-319-18660-3

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Hardcover ISBN: 978-3-319-18659-7Published: 21 July 2015

  • Softcover ISBN: 978-3-319-36157-4Published: 15 October 2016

  • eBook ISBN: 978-3-319-18660-3Published: 08 July 2015

  • Series ISSN: 1050-6977

  • Series E-ISSN: 2297-0428

  • Edition Number: 1

  • Number of Pages: X, 340

  • Number of Illustrations: 31 b/w illustrations, 21 illustrations in colour

  • Topics: Probability Theory and Stochastic Processes, Geometry, Measure and Integration

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