Recent Developments in Fractals and Related Fields : Conference on Fractals and Related Fields III, île de Porquerolles, France, 2015

Description

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. Read more... Abstract: 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 Front Matter ....Pages i-xii New Exponents for Pointwise Singularity Classification (Patrice Abry, Stéphane Jaffard, Roberto Leonarduzzi, Clothilde Melot, Herwig Wendt)....Pages 1-37 The Two-Dimensional Density of Bernoulli Convolutions (Christoph Bandt)....Pages 39-55 Iterated Functions Systems, Blenders, and Parablenders (Pierre Berger, Sylvain Crovisier, Enrique Pujals)....Pages 57-70 Multifractal Properties of Convex Hulls of Typical Continuous Functions (Zoltán Buczolich)....Pages 71-86 Fourier Bases and Fourier Frames on Self-Affine Measures (Dorin Ervin Dutkay, Chun-Kit Lai, Yang Wang)....Pages 87-111 Self-Similar Sets: Projections, Sections and Percolation (Kenneth Falconer, Xiong Jin)....Pages 113-127 Some Problems on the Boundary of Fractal Geometry and Additive Combinatorics (Michael Hochman)....Pages 129-174 Random Covering Sets, Hitting Probabilities and Variants of the Covering Problem (Maarit Järvenpää)....Pages 175-187 Small Union with Large Set of Centers (Tamás Keleti)....Pages 189-206 Some Recent Developments of Self-Affine Tiles (Chun-Kit Lai, Ka-Sing Lau)....Pages 207-232 A Class of Random Cantor Measures, with Applications (Pablo Shmerkin, Ville Suomala)....Pages 233-260 A Survey on the Dimension Theory in Dynamical Diophantine Approximation (Baowei Wang, Jun Wu)....Pages 261-294 (S)PDE on Fractals and Gaussian Noise (Martina Zähle)....Pages 295-312