**Proceedings of Symposia in Pure Mathematics**

Volume: 72;
2004;
517 pp;
Hardcover

MSC: Primary 28; 11; 37; 60; 68; 82;

Print ISBN: 978-0-8218-3637-8

Product Code: PSPUM/72.1

List Price: $120.00

Individual Member Price: $96.00

**Electronic ISBN: 978-0-8218-9377-7
Product Code: PSPUM/72.1.E**

List Price: $120.00

Individual Member Price: $96.00

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# Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot: Analysis, Number Theory, and Dynamical Systems

Share this page *Edited by *
*Michel L. Lapidus; Machiel van Frankenhuijsen*

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.

#### Table of Contents

# Table of Contents

## Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot: Analysis, Number Theory, and Dynamical Systems

- Contents v6
- Part 1. Analysis, Number Theory, and Dynamical Systems iii4 free
- Preface ix10 free
- List of Tributes xi12 free
- Fractal geometry and applications—An introduction to this volume 114 free
- Tributes 2740
- ANALYSIS 6578
- Reflections, ripples and fractals 6780
- Lacunarity, Minkowski content, and self-similar sets in R 7790
- Fractals and geometric measure theory: Friends and foes 93106
- Eigenmeasures, equidistribution, and the multiplicity of β-expansions 97110
- Distances on topological self-similar sets 117130
- Energy and Laplacian on the Sierpinki gasket 131144
- Electrical networks, symplectic reductions, and application to the renormalization map of self-similar lattices 155168
- Notes on Bernoulli convolutions 207220

- NUMBER THEORY 231244
- DYNAMICAL SYSTEMS 373386
- The invariant fractals of symplectic piecewise affine elliptic dynamics 375388
- Almost sure rotation number of circle endomorphisms 391404
- Kneading determinants and transfer operators in higher dimensions 407420
- The spectrum of dimensions for Poincaré recurrences for nonuniformly hyperbolic geometric constructions 417430
- A Survey of results in random iteration 435448
- On fibers and local connectivity of Mandelbrot and Multibrot sets 477490

#### Readership

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