Recent Developments in Fractals and Related Fields

1. Front Matter

   Pages i-xii

   PDF

2. New Exponents for Pointwise Singularity Classification

   • Patrice Abry, Stéphane Jaffard, Roberto Leonarduzzi, Clothilde Melot, Herwig Wendt

   Pages 1-37

3. The Two-Dimensional Density of Bernoulli Convolutions

   • Christoph Bandt

   Pages 39-55

4. Iterated Functions Systems, Blenders, and Parablenders

   • Pierre Berger, Sylvain Crovisier, Enrique Pujals

   Pages 57-70

5. Multifractal Properties of Convex Hulls of Typical Continuous Functions

   • Zoltán Buczolich

   Pages 71-86

6. Fourier Bases and Fourier Frames on Self-Affine Measures

   • Dorin Ervin Dutkay, Chun-Kit Lai, Yang Wang

   Pages 87-111

7. Self-Similar Sets: Projections, Sections and Percolation

   • Kenneth Falconer, Xiong Jin

   Pages 113-127

8. Some Problems on the Boundary of Fractal Geometry and Additive Combinatorics

   • Michael Hochman

   Pages 129-174

9. Random Covering Sets, Hitting Probabilities and Variants of the Covering Problem

   • Maarit Järvenpää

   Pages 175-187

10. Small Union with Large Set of Centers

    • Tamás Keleti

    Pages 189-206

11. Some Recent Developments of Self-Affine Tiles

    • Chun-Kit Lai, Ka-Sing Lau

    Pages 207-232

12. A Class of Random Cantor Measures, with Applications

    • Pablo Shmerkin, Ville Suomala

    Pages 233-260

13. A Survey on the Dimension Theory in Dynamical Diophantine Approximation

    • Baowei Wang, Jun Wu

    Pages 261-294

14. (S)PDE on Fractals and Gaussian Noise

    • Martina Zähle

    Pages 295-312

This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions,  as well as surveys from many of the leading experts on modern fractal theory and applications. It is an outgrowth of the Conference of Fractals and Related Fields III, that was held on September 19-25, 2015 in île de Porquerolles, France. Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing. The book is aimed at pure and applied mathematicians in these areas, as well as other researchers interested in discovering the fractal domain.

• Applications of Fractala
• Dynamical Systems
• Ergodic Theory
• Functional Analysis
• Geometric Measure Theory
• Probability & Stochastic Processes
• combinatorics

• Laboratoire Analyse, Géométrie et Applications, Université Paris 13, Villetaneuse, France

  Julien Barral

• Laboratoire d’Analyse et de Mathématiques Appliquées (UMR 8050), Université Paris-Est, UPEMLV, UPEC, CNRS, Créteil, France

  Stéphane Seuret

Policies and ethics