Recent Developments in Fractals and Related Fields

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

Julien Barral, Stéphane Seuret (Herausgeber)

Buch | Hardcover

XII, 312 Seiten

2017 | 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-57803-3 (ISBN)

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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.

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).

Erscheinungsdatum	22.09.2017
Reihe/Serie	Trends in Mathematics
Zusatzinfo	XII, 312 p. 31 illus., 15 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	649 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Applications of Fractala • combinatorics • combinatorics & graph theory • Combinatorics & graph theory • Dynamical Systems • Dynamical Systems and Ergodic Theory • ergodic theory • Functional Analysis • Functional analysis & transforms • Functional analysis & transforms • geometric measure theory • Integral calculus & equations • Integral calculus & equations • Mathematics • mathematics and statistics • measure and integration • Nonlinear Science • Number Theory • probability & statistics • Probability & Stochastic Processes • Probability & statistics • Probability & Stochastic Processes • Probability theory and stochastic processes • stochastics
ISBN-10	3-319-57803-0 / 3319578030
ISBN-13	978-3-319-57803-3 / 9783319578033
Zustand	Neuware