Fractal Geometry and Stochastics V

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

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.

• fractal structures
• geometric measure theory
• multifractal analysis
• probabilistic analysis
• recursive constructions

• 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

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