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Recent Developments in Fractals and Related Fields

Conference on Fractals and Related Fields III, île de Porquerolles, France, 2015

  • Conference proceedings
  • © 2017

Overview

Editors:
  1. Julien Barral

    1. Laboratoire Analyse, Géométrie et Applications, Université Paris 13, Villetaneuse, France

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  2. Stéphane Seuret

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

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    You can also search for this editor in PubMed   Google Scholar

  • Provides an overview of recent developments in mathematical fields related to fractals
  • Includes original research contributions as well as surveys written by experts in their respective fields
  • Readers will find interesting and motivating results as well as new avenues for further research?
  • Includes supplementary material: sn.pub/extras
  • Includes supplementary material: sn.pub/extras

Part of the book series: Trends in Mathematics (TM)

Included in the following conference series:

Conference proceedings info: FARF3 2015.

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Table of contents (13 papers)

  1. Front Matter

    Pages i-xii
    Download chapter 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
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  1. Recent Developments in Fractals and Related Fields

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About this book

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.

Editors and Affiliations

  • 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

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