Fractal Geometry and Analysis

Softcover Nachdruck of the original 1. Auflage 1991
ISBN: 978-94-015-7933-9
Verlag: Springer Netherlands

Buch, Englisch, 472 Seiten, Format (B × H): 160 mm x 240 mm, Gewicht: 779 g

Reihe: Nato Science Series C:

This ASI- which was also the 28th session of the Seminaire de mathematiques superieures of the Universite de Montreal - was devoted to Fractal Geometry and Analysis. The present volume is the fruit of the work of this Advanced Study Institute. We were fortunate to have with us Prof. Benoit Mandelbrot - the creator of numerous concepts in Fractal Geometry - who gave a series of lectures on multifractals, iteration of analytic functions, and various kinds of fractal stochastic processes. Different foundational contributions for Fractal Geometry like measure theory, dy namical systems, iteration theory, branching processes are recognized. The geometry of fractal sets and the analytical tools used to investigate them provide a unifying theme of this book. The main topics that are covered are then as follows. Dimension Theory. Many definitions of fractional dimension have been proposed, all of which coincide on "regular" objects, but often take different values for a given fractal set. There is ample discussion on piecewise estimates yielding actual values for the most common dimensions (Hausdorff, box-counting and packing dimensions). The dimension theory is mainly discussed by Mendes-France, Bedford, Falconer, Tricot and Rata. Construction of fractal sets. Scale in variance is a fundamental property of fractal sets.

Zielgruppe

Research

Autoren/Hrsg.

Dubuc, Serge

Bélair, Jacques

Fachgebiete

• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

Applications of dynamical systems theory to fractals — a study of cookie-cutter Cantor sets.- Complex dynamics: an informal discussion.- Substitutions, branching processes and fractal sets.- Interpolation fractale.- Dimensions — their determination and properties.- Topological aspects of self-similar sets and singular functions.- Produits de poids aléatoires indépendants et applications.- The Planck constant of a curve.- Rectifiable and fractal sets.- Iterated function systems: theory, applications and the inverse problem.