Recent Developments in Fractals and Related Fields

  • Julien Barral
  • Stéphane Seuret

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Geometric Measure Theory and Multifractals

    1. Front Matter
      Pages 1-1
    2. Stéphane Jaffard, Samuel Nicolay
      Pages 19-34
    3. Esa Järvenpää
      Pages 35-43
    4. Antti Käenmäki
      Pages 45-54
    5. Jörg Schmeling, Pablo Shmerkin
      Pages 55-72
    6. Steffen Winter
      Pages 73-89
  3. Harmonic and Functional Analysis and, Signal Processing

    1. Front Matter
      Pages 91-91
    2. Aline Bonami, Szilárd Gy. Révész
      Pages 107-129
    3. Henning Kempka
      Pages 191-201
    4. Michel Mendès France, Ahmed Sebbar
      Pages 203-206
    5. Dominique Pastor, Abdourrahmane M. Atto
      Pages 207-232
  4. Dynamical Systems and Analysis on Fractals

    1. Front Matter
      Pages 233-233
    2. Christoph Bandt
      Pages 235-249
    3. Ai Hua Fan, Thomas Langlet, Bing Li
      Pages 251-266
    4. Xin-Han Dong, Ka-Sing Lau
      Pages 283-294
  5. Stochastic Processes and Random Fractals

    1. Front Matter
      Pages 309-309
    2. Antoine Ayache, Pierre R. Bertrand
      Pages 311-326
    3. Arnaud Durand
      Pages 343-351
    4. Edward C. Waymire, Stanley C. Williams
      Pages 353-380
  6. Combinatorics on Words

    1. Front Matter
      Pages 381-381
    2. Jean-Paul Allouche, Zhi-Xiong Wen
      Pages 383-391
    3. Hui Rao, Zhi-Ying Wen
      Pages 401-409
    4. Zhi-Xiong Wen
      Pages 411-419
  7. Back Matter
    Pages 421-422

About this book


This book—an outgrowth of an international conference held in honor of Jacques Peyrière—provides readers with an overview of recent developments in the mathematical fields related to fractals. Included are original research contributions as well as surveys written by experts in their respective fields.

The chapters are thematically organized into five major sections:

• Geometric Measure Theory and Multifractals;

• Harmonic and Functional Analysis and Signal Processing;

• Dynamical Systems and Analysis on Fractals;

• Stochastic Processes and Random Fractals;

• Combinatorics on Words.

Recent Developments in Fractals and Related Fields is aimed at pure and applied mathematicians working in the above-mentioned areas as well as other researchers interested in discovering the fractal domain. Throughout the volume, readers will find interesting and motivating results as well as new avenues for further research.


J.-P. Allouche, A.M. Atto, J.-M. Aubry, F. Axel, A. Ayache, C. Bandt, F. Bastin, P.R. Bertrand, A. Bonami, G. Bourdaud, Z. Buczolich, M. Clausel, Y. Demichel, X.-H. Dong, A. Durand, A.H. Fan, U.R. Freiberg, S. Jaffard, E. Järvenpää, A. Käenmäki, A. Karoui, H. Kempka, T. Langlet, K.-S. Lau, B. Li, M.M. France, S. Nicolay, E. Olivier, D. Pastor, H. Rao, S.Gy. Révész, J. Schmeling, A. Sebbar, P. Shmerkin, E.C. Waymire, Z.-X. Wen, Z.-Y. Wen, S.C. Williams, S. Winter


Brownian motion Martingale analysis on fractals combinatorics on words ergodic theory and dynamical systems fractional Brownian motion functional analysis geometric measure theory harmonic analysis linear optimization mixing stochastic process stochastic processes

Editors and affiliations

  • Julien Barral
    • 1
  • Stéphane Seuret
    • 2
  1. 1.Département de MathématiquesLAGA (UMR CNRS 7539)VilletaneuseFrance
  2. 2.Université Paris-EstLaboratoire d'Analyse et de MathématiqueCRETEIL CedexFrance

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