Overview

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.

Full Product Details

Author:   Julien Barral ,  Stéphane Seuret
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   1st ed. 2017
Weight:   6.092kg
ISBN:  

9783319578033

ISBN 10:   3319578030
Pages:   312
Publication Date:   21 September 2017
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

New exponents for pointwise singularity classification (Abry, Jaffard, Leonarduzzi, Melot, Wendt).- The two-dimensional density of Bernoulli Convolutions (Bandt).- Iterated Functions Systems, Blenders and Parablenders (Berger, Crovisier, Pujals).- Multifractal properties of convex hulls of typical continuous functions (Buczolich).- Fourier bases and Fourier frames on self-affine measures (Dutkay, Lai, Wang).- Self-similar sets: Projections, Sections and Percolation (Falconer, Jin).- Some problems on the boundary of fractal geometry and additive combinatorics (Hochman).- Random covering sets, hitting probabilities and variants of the covering problem (Järvenpää).- Small Union with Large Set of Centers (Keleti).- Some Recent developments of self-affine tiles (Lai, Lau).- A class of random Cantor measures, with applications (Shmerkin, Suomala).- A survey on the dimension theory in dynamical Diophantine approximation (Wang, Wu).- (S)PDE on Fractals and Gaussian Noise (Zähle).

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