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Fractal geometry and applications : a jubilee of Benoît Mandelbrot : analysis, number theory, and dynamical systems / Michel L. Lapidus (managing editor), Machiel van Frankenhuijsen, editors.
- Format:
- Book
- Series:
- Proceedings of symposia in pure mathematics ; volume 72, part 1.
- Proceedings of symposia in pure mathematics ; volume 72, part 1
- Language:
- English
- Subjects (All):
- Measure theory--Congresses.
- Measure theory.
- Fractals--Congresses.
- Fractals.
- Ergodic theory--Congresses.
- Ergodic theory.
- Physical Description:
- 1 online resource (534 p.)
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, [2004]
- Language Note:
- English
- Summary:
- 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:
- ""Contents""; ""Part 1. Analysis, Number Theory, and Dynamical Systems""; ""Preface""; ""List of Tributes""; ""Fractal geometry and applications�An introduction to this volume""; ""Tributes""; ""ANALYSIS""; ""Reflections, ripples and fractals""; ""Lacunarity, Minkowski content, and self-similar sets in R""; ""Fractals and geometric measure theory: Friends and foes""; ""Distances on topological self-similar sets""; ""Energy and Laplacian on the Sierpinki gasket""; ""Electrical networks, symplectic reductions, and application to the renormalization map of self-similar lattices""
- ""Notes on Bernoulli convolutions""""NUMBER THEORY""; ""Some connections between Bernoulli convolutions and analytic number theory""; ""On Davenport expansions""; ""Hausdorff dimension and Diophantine approximation""; ""Fractality, self-similarity and complex dimensions""; ""DYNAMICAL SYSTEMS""; ""The invariant fractals of symplectic piecewise affine elliptic dynamics""; ""Almost sure rotation number of circle endomorphisms""; ""Kneading determinants and transfer operators in higher dimensions""
- Notes:
- Description based upon print version of record.
- Includes bibliographical references.
- Description based on online resource; title from PDF title page (ebrary, viewed May 19, 2014).
- ISBN:
- 0-8218-9377-7
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