This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry.

In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications.

This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.

Readership

Graduate students and research mathematicians interested in fractal geometry and its applications.

Table of Contents

• J. Barral and B. B. Mandelbrot -- Introduction to infinite products of independent random functions (Random multiplicative multifractal measures, part I)
• J. Barral and B. B. Mandelbrot -- Non-degeneracy, moments, dimension, and multifractal analysis for random multiplicative measures (Random multiplicative multifractal measures, part II)
• J. Barral -- Techniques for the study of infinite products of independent random functions (Random multiplicative multifractal measures, part III)
• S. P. Jaffard -- Wavelet techniques in multifractal analysis
• J. L. Véhel and S. Seuret -- The 2-microlocal formalism
• J. Peyrière -- A vectorial multifractal formalism

• B. M. Hambly and T. Kumagai -- Heat kernel estimates for symmetric random walks on a class of fractal graphs and stability under rough isometries
• Y. Xiao -- Random fractals and Markov processes
• G. F. Lawler, O. Schramm, and W. Werner -- On the scaling limit of planar self-avoiding walk
• B. Duplantier -- Conformal fractal geometry & boundary quantum gravity

• A. Desolneux, B. Sapoval, and A. Baldassarri -- Self-organized percolation power laws with and without fractal geometry in the etching of random solids
• M.-O. Coppens -- Nature inspired chemical engineering-Learning from the fractal geometry of nature in sustainable chemical engineering
• F. K. Musgrave -- Fractal forgeries of nature