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Fractal Geometryby Kenneth Falconer
John Wiley & Sons, Ltd. 2004; US$ 205.00Since its original publication in 1990, Kenneth Falconer's Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines. This new edition has been extensively revised and updated. It features much new material, many additional exercises, notes and references, and an extended bibliography that reflects the development of the subject since the first edition. * Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals. * Each topic is carefully explained and illustrated by examples and figures.... more...
Multifractalsby David Harte
CRC Press 2001; US$ 99.95Although multifractal measures are rooted in probability theory, much of the literature is found in physics and mathematics. Harte, a statistician and earthquake forecaster in New Zealand, pulls together ideas from multiple disciplines to place the material into a probabilistic and statistical context, using language familiar to statistical scienti more...
Fractal Dimensions for Poincare Recurrencesby Valentin Afraimovich; Edgardo Ugalde; Jesus Urias
Elsevier 2006; US$ 185.00This book is devoted to an important branch of the dynamical systems theory : the study of the fine (fractal) structure of Poincare recurrences -instants of time when the system almost repeats its initial state. The authors were able to write an entirely self-contained text including many insights and examples, as well as providing complete details of proofs. The only prerequisites are a basic knowledge of analysis and topology. Thus this book can serve as a graduate text or self-study guide for courses in applied mathematics or nonlinear dynamics (in the natural sciences). Moreover, the book can be used by specialists in applied nonlinear dynamics following the way in the book. The authors applied the mathematical theory developed in the... more...
Fractal Geometry, Complex Dimensions and Zeta Functionsby Michel L. Lapidus; Machiel Frankenhuijsen
Springer 2006; US$ 69.95Offers a study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. This book interlinks number theory, spectral geometry, and fractal geometry. It gives the Riemann hypothesis a natural geometric reformulation in the context of vibrating fractal strings. It includes theorems, examples and illustrations. more...
Fractals and Universal Spaces in Dimension Theoryby Stephen Lipscomb
Springer 2009; US$ 79.95Historically, for metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research. The history breaks naturally into two periods - the classical (separable metric) and the modern (not-necessarily separable metric). This book unifies the modern theory from 1960-2007. more...
Computability of Julia Setsby Mark Braverman; Michael Yampolsky
Springer 2008; US$ 89.95Among all computer-generated mathematical images, Julia sets of rational maps occupy one of the most prominent positions. This book summarizes the knowledge about the computational properties of Julia sets in a self-contained way. It is suitable for experts and students with interest in theoretical computer science or dynamical systems. more...
A Random Walk Through Fractal Dimensionsby Brian H. Kaye
Wiley-VCH 2008; US$ 73.95Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science. From reviews of the first edition: '...no stone is left unturned in the quest for applications of fractal... more...
Recent Developments in Fractals and Related Fieldsby Julien Barral; Stephane Seuret
Springer 2010; US$ 149.00This book - an outgrowth of an international conference held in honor of Jacques Peyriere - provides readers with an overview of recent developments in the mathematical fields related to fractals. Included are original research contributions as well as surveys written by experts in their respective fields. The chapters are thematically organized into five major sections: Geometric Measure Theory and Multifractals; Harmonic and Functional Analysis and Signal Processing; Dynamical Systems and Analysis on Fractals; Stochastic Processes and Random Fractals; and, Combinatorics on Words. Recent Developments in Fractals and Related Fields is aimed at pure and applied mathematicians working in the above-mentioned areas as well as other researchers... more...
The Colours of Infinityby Nigel Lesmoir-Gordon
Springer 2011; US$ 59.95The groundbreaking documentary (accompanying this book), introduced by Arthur C. Clarke, has been shown in over 50 countries around the world. Twenty five years ago it brought the subject of fractals to the attention of the general public for the first time. The contributors to the film are joined in this comprehensive survey of fractal theory and practice by some other leading experts in the field. Beautifully and copiously illustrated, this latest edition also comes with an e-copy of the groundbreaking TV documentary. It brings fractal geometry up to date by gathering the thoughts and enthusiasms of the foremost writers and researchers in the field. A new chapter from Benoit Mandelbrot, the mathematician and founder of fractal geometry, makes... more...
The Mandelbrot Set, Theme and Variationsby Tan Lei
Cambridge University Press 2000; US$ 88.00Systematic exposition of current knowledge about the Mandelbrot set, discussing the latest research and results. more...
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