Proceedings of Symposia in Pure Mathematics 2004; 1091 pp; hardcover Volume: 72 ISBN10: 0821832921 ISBN13: 9780821832929 List Price: US$186 Member Price: US$148.80 Order Code: PSPUM/72
 This volume offers an excellent selection of cuttingedge 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 highquality contributions to the volume by wellknown researchersincluding two articles by Mandelbrotprovide a solid crosssection 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 twopart 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 Part I  M. L. Lapidus  Fractal geometry and applicationsAn introduction to this volume
 J. Barral and S. Jaffard  Cherche Livre... et plus si affinité/Looking for a book...and more, if affinity
 M. Berry  Benefiting from fractals
 M.O. Coppens  Benoit Mandelbrot, wizard of science
 R. L. Devaney  Mandelbrot's vision for mathematics
 M. M. Dodson  Benoit Mandelbrot and York
 B. Duplantier  Nul n'entre ici s'il n'est géomètre/Let no one ignorant of geometry enter here
 M. L. Frame  A decade of working with a maverick
 M. Frantz  Breakfast with Mandelbrot
 J.P. Kahane  Old memories
 D. B. Mumford  My encounters with Benoit Mandelbrot
 L. Nottale  Fractal geometry and the foundations of physics
 B. Sapoval  Is randomness partially tamed by fractals?
 J. E. Taylor  On knowing Benoit Mandelbrot
Analysis  M. M. France  Reflections, ripples and fractals
 M. Frantz  Lacunarity, Minkowski content, and selfsimilar sets in \(\mathbb{R}\)
 F. Morgan  Fractals and geometric measure theory: Friends and foes
 H. Furstenberg and Y. Katznelson  Eigenmeasures, equidistribution, and the multiplicity of \(\beta\)expansions
 A. Kameyama  Distances on topological selfsimilar sets
 A. Teplyaev  Energy and laplacian on the Sierpiński gasket
 C. Sabot  Electrical networks, symplectic reductions, and application to the renormalization map of selfsimilar lattices
 B. Solomyak  Notes on Bernoulli convolutions
Number theory  T. Hilberdink  Some connections between Bernoulli convolutions and analytic number theory
 S. Jaffard  On Davenport expansions
 M. M. Dodson and S. Kristensen  Hausdorff dimension and diophantine approximation
 M. L. Lapidus and M. van Frankenhuijsen  Fractality, selfsimilarity and complex dimensions
Dynamical systems  B. Kahng  The invariant fractals of symplectic piecewise affine elliptic dynamics
 S. Crovisier  Almost sure rotation number of circle endomorphisms
 V. Baladi  Kneading determinants and transfer operators in higher dimensions
 V. Afraimovich, L. Ramírez, and E. Ugalde  The spectrum of dimensions for Poincaré recurrences for nonuniformly hyperbolic geometric constructions
 M. Comerford  A survey of results in random iteration
 D. Schleicher  On fibers and local connectivity of Mandelbrot and multibrot sets
Part II Multifractals  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  Nondegeneracy, 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 2microlocal formalism
 J. Peyrière  A vectorial multifractal formalism
Probability and statistical mechanics  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 selfavoiding walk
 B. Duplantier  Conformal fractal geometry & boundary quantum gravity
Applications  A. Desolneux, B. Sapoval, and A. Baldassarri  Selforganized percolation power laws with and without fractal geometry in the etching of random solids
 M.O. Coppens  Nature inspired chemical engineeringLearning from the fractal geometry of nature in sustainable chemical engineering
 F. K. Musgrave  Fractal forgeries of nature
