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| Hardcover ISBN: | 978-0-8218-3637-8 |
| Product Code: | PSPUM/72.1 |
| List Price: | $139.00 |
| MAA Member Price: | $125.10 |
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| eBook ISBN: | 978-0-8218-9377-7 |
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Book DetailsProceedings of Symposia in Pure MathematicsVolume: 72; 2004; 517 ppMSC: Primary 28; 11; 37; 60; 68; 82
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.
ReadershipGraduate students and research mathematicians interested in fractal geometry and its applications.
This item is also available as part of a set: -
Table of Contents
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Articles
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Michel L. Lapidus — Fractal geometry and applications—An introduction to this volume
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Analysis
-
Michel Mendès France — Reflections, ripples and fractals [ MR 2112100 ]
-
Marc Frantz — Lacunarity, Minkowski content, and self-similar sets in $\mathbb {R}$ [ MR 2112101 ]
-
Frank Morgan — Fractals and geometric measure theory: friends and foes [ MR 2112102 ]
-
Hillel Furstenberg and Yitzhak Katznelson — Eigenmeasures, equidistribution, and the multiplicity of $\beta $-expansions [ MR 2112103 ]
-
Atsushi Kameyama — Distances on topological self-similar sets [ MR 2112104 ]
-
Alexander Teplyaev — Energy and Laplacian on the Sierpiński gasket [ MR 2112105 ]
-
Christophe Sabot — Electrical networks, symplectic reductions, and application to the renormalization map of self-similar lattices [ MR 2112106 ]
-
Boris Solomyak — Notes on Bernoulli convolutions [ MR 2112107 ]
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Number theory
-
Titus Hilberdink — Some connections between Bernoulli convolutions and analytic number theory [ MR 2112108 ]
-
Stéphane Jaffard — On Davenport expansions [ MR 2112109 ]
-
M. Maurice Dodson and Simon Kristensen — Hausdorff dimension and Diophantine approximation [ MR 2112110 ]
-
Michel L. Lapidus and Machiel van Frankenhuijsen — Fractality, self-similarity and complex dimensions [ MR 2112111 ]
-
Dynamical systems
-
Byungik Kahng — The invariant fractals of symplectic piecewise affine elliptic dynamics [ MR 2112112 ]
-
Sylvain Crovisier — Almost sure rotation number of circle endomorphisms [ MR 2112113 ]
-
Viviane Baladi — Kneading determinants and transfer operators in higher dimensions [ MR 2112114 ]
-
Valentin Afraimovich, Leticia Ramírez and Edgardo Ugalde — The spectrum of dimensions for Poincaré recurrences for nonuniformly hyperbolic geometric constructions [ MR 2112115 ]
-
Mark Comerford — A survey of results in random iteration [ MR 2112116 ]
-
Dierk Schleicher — On fibers and local connectivity of Mandelbrot and Multibrot sets [ MR 2112117 ]
-
-
RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
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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.
Graduate students and research mathematicians interested in fractal geometry and its applications.
-
Articles
-
Michel L. Lapidus — Fractal geometry and applications—An introduction to this volume
-
Analysis
-
Michel Mendès France — Reflections, ripples and fractals [ MR 2112100 ]
-
Marc Frantz — Lacunarity, Minkowski content, and self-similar sets in $\mathbb {R}$ [ MR 2112101 ]
-
Frank Morgan — Fractals and geometric measure theory: friends and foes [ MR 2112102 ]
-
Hillel Furstenberg and Yitzhak Katznelson — Eigenmeasures, equidistribution, and the multiplicity of $\beta $-expansions [ MR 2112103 ]
-
Atsushi Kameyama — Distances on topological self-similar sets [ MR 2112104 ]
-
Alexander Teplyaev — Energy and Laplacian on the Sierpiński gasket [ MR 2112105 ]
-
Christophe Sabot — Electrical networks, symplectic reductions, and application to the renormalization map of self-similar lattices [ MR 2112106 ]
-
Boris Solomyak — Notes on Bernoulli convolutions [ MR 2112107 ]
-
Number theory
-
Titus Hilberdink — Some connections between Bernoulli convolutions and analytic number theory [ MR 2112108 ]
-
Stéphane Jaffard — On Davenport expansions [ MR 2112109 ]
-
M. Maurice Dodson and Simon Kristensen — Hausdorff dimension and Diophantine approximation [ MR 2112110 ]
-
Michel L. Lapidus and Machiel van Frankenhuijsen — Fractality, self-similarity and complex dimensions [ MR 2112111 ]
-
Dynamical systems
-
Byungik Kahng — The invariant fractals of symplectic piecewise affine elliptic dynamics [ MR 2112112 ]
-
Sylvain Crovisier — Almost sure rotation number of circle endomorphisms [ MR 2112113 ]
-
Viviane Baladi — Kneading determinants and transfer operators in higher dimensions [ MR 2112114 ]
-
Valentin Afraimovich, Leticia Ramírez and Edgardo Ugalde — The spectrum of dimensions for Poincaré recurrences for nonuniformly hyperbolic geometric constructions [ MR 2112115 ]
-
Mark Comerford — A survey of results in random iteration [ MR 2112116 ]
-
Dierk Schleicher — On fibers and local connectivity of Mandelbrot and Multibrot sets [ MR 2112117 ]
