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Full Description
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.
Contents
Fractal geometry and applications-An introduction to this volume by M. L. Lapidus Cherche Livre... et plus si affinite/Looking for a book...and more, if affinity by J. Barral and S. Jaffard Benefiting from fractals by M. Berry Benoit Mandelbrot, wizard of science by M.-O. Coppens Mandelbrot's vision for mathematics by R. L. Devaney Benoit Mandelbrot and York by M. M. Dodson Nul n'entre ici s'il n'est geometre/Let no one ignorant of geometry enter here by B. Duplantier A decade of working with a maverick by M. L. Frame Breakfast with Mandelbrot by M. Frantz Old memories by J.-P. Kahane My encounters with Benoit Mandelbrot by D. B. Mumford Fractal geometry and the foundations of physics by L. Nottale Is randomness partially tamed by fractals? by B. Sapoval On knowing Benoit Mandelbrot by J. E. Taylor Analysis: Reflections, ripples and fractals by M. M. France Lacunarity, Minkowski content, and self-similar sets in $\mathbb{R}$ by M. Frantz Fractals and geometric measure theory: Friends and foes by F. Morgan Eigenmeasures, equidistribution, and the multiplicity of $\beta$-expansions by H. Furstenberg and Y. Katznelson Distances on topological self-similar sets by A. Kameyama Energy and laplacian on the Sierpinski gasket by A. Teplyaev Electrical networks, symplectic reductions, and application to the renormalization map of self-similar lattices by C. Sabot Notes on Bernoulli convolutions by B. Solomyak Number theory: Some connections between Bernoulli convolutions and analytic number theory by T. Hilberdink On Davenport expansions by S. Jaffard Hausdorff dimension and diophantine approximation by M. M. Dodson and S. Kristensen Fractality, self-similarity and complex dimensions by M. L. Lapidus and M. van Frankenhuijsen Dynamical systems: The invariant fractals of symplectic piecewise affine elliptic dynamics by B. Kahng Almost sure rotation number of circle endomorphisms by S. Crovisier Kneading determinants and transfer operators in higher dimensions by V. Baladi The spectrum of dimensions for Poincare recurrences for nonuniformly hyperbolic geometric constructions by V. Afraimovich, L. Ramirez, and E. Ugalde A survey of results in random iteration by M. Comerford On fibers and local connectivity of Mandelbrot and multibrot sets by D. Schleicher.
