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

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.

List 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).

Summary

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

Product details

• Assisted by: Julie Barral (Editor), Julien Barral (Editor), Seuret (Editor), Seuret (Editor), Stéphane Seuret (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2018
• EAN: 9783319862545
• ISBN: 978-3-31-986254-5
• No. of pages: 312
• Dimensions: 155 mm x 17 mm x 235 mm
• Weight: 498 g
• Illustrations: XII, 312 p. 31 illus., 15 illus. in color.
• Series: Trends in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; C, measure theory, Combinatorics, Dynamics, Mathematics and Statistics, Functional Analysis, Probability Theory and Stochastic Processes, Discrete Mathematics, Number Theory, Probability & statistics, Combinatorics & graph theory, Dynamical Systems and Ergodic Theory, Ergodic theory, Dynamical systems, Probabilities, Stochastics, Probability Theory, Integral calculus & equations, Functional analysis & transforms, Measure and Integration