Описание: Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.Key Features: - The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings- Complex dimensions of a fractal string, defined as the poles of an associated zeta function, are studied in detail, then used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra- Explicit formulas are extended to apply to the geometric, spectral, and dynamic zeta functions associated with a fractal- Examples of such formulas include Prime Orbit Theorem with error term for self-similar flows, and a tube formula- The method of diophantine approximation is used to study self-similar strings and flows- Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functionsThroughout new results are examined. The final chapter gives a new definition of fractality as the presence of nonreal complex dimensions with positive real parts.The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics.
Автор: Massopust, Peter R. Название: Fractal Functions, Fractal Surfaces, and Wavelets ISBN: 012804408X ISBN-13(EAN): 9780128044087 Издательство: Elsevier Science Рейтинг: Цена: 12462.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Fractal Functions, Fractal Surfaces, and Wavelets, Second Edition, is the first systematic exposition of the theory of local iterated function systems, local fractal functions and fractal surfaces, and their connections to wavelets and wavelet sets. The book is based on Massopust’s work on and contributions to the theory of fractal interpolation, and the author uses a number of tools—including analysis, topology, algebra, and probability theory—to introduce readers to this exciting subject. . Though much of the material presented in this book is relatively current (developed in the past decades by the author and his colleagues) and fairly specialized, an informative background is provided for those entering the field. With its coherent and comprehensive presentation of the theory of univariate and multivariate fractal interpolation, this book will appeal to mathematicians as well as to applied scientists in the fields of physics, engineering, biomathematics, and computer science. In this second edition, Massopust includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, further develops the connections to wavelets and wavelet sets, and deepens and extends the pedagogical content.
Автор: Falconer Kenneth Название: Fractal Geometry ISBN: 111994239X ISBN-13(EAN): 9781119942399 Издательство: Wiley Рейтинг: Цена: 6803.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This comprehensive and popular textbook makes fractal geometry accessible to final-year undergraduate math or physics majors, while also serving as a reference for research mathematicians or scientists. This up-to-date edition covers introductory multifractal theory, random fractals, and modern applications in finance and science.
Автор: Christoph Bandt; Kenneth Falconer; Martina Z?hle Название: Fractal Geometry and Stochastics V ISBN: 3319186590 ISBN-13(EAN): 9783319186597 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book collects significant contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five topical sections: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions.
Автор: Michel L. Lapidus; Machiel van Frankenhuysen Название: Fractal Geometry and Number Theory ISBN: 0817640983 ISBN-13(EAN): 9780817640989 Издательство: Springer Рейтинг: Цена: 12577.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Number theory and fractal geometry are combined in this study of the vibrations of fractal strings. The book centres around a notion of complex dimension extended here to apply to the zeta functions associated with fractals.
Автор: Christoph Bandt; Peter M?rters; Martina Z?hle Название: Fractal Geometry and Stochastics IV ISBN: 3034600291 ISBN-13(EAN): 9783034600293 Издательство: Springer Рейтинг: Цена: 18167.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This process has been forced by problems in these areas related to applications in statistical physics, biomathematics and finance.This book is a collection of survey articles covering many of the most recent developments, like Schramm-Loewner evolution, fractal scaling limits, exceptional sets for percolation, and heat kernels on fractals.
Автор: Gerald Edgar Название: Measure, Topology, and Fractal Geometry ISBN: 1441925694 ISBN-13(EAN): 9781441925695 Издательство: Springer Рейтинг: Цена: 5723.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
From reviews of the first edition:
"In the world of mathematics, the 1980's might well be described as the "decade of the fractal." Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology...the book also contains many good illustrations of fractals (including 16 color plates)."
Mathematics Teaching
"The book can be recommended to students who seriously want to know about the mathematical foundation of fractals, and to lecturers who want to illustrate a standard course in metric topology by interesting examples."
Christoph Bandt, Mathematical Reviews
..".not only intended to fit mathematics students who wish to learn fractal geometry from its beginning but also students in computer science who are interested in the subject. Especially, for the last students the author gives the required topics from metric topology and measure theory on an elementary level. The book is written in a very clear style and contains a lot of exercises which should be worked out."
H.Haase, Zentralblatt
About the second edition: Changes throughout the text, taking into account developments in the subject matter since 1990; Major changes in chapter 6. Since 1990 it has become clear that there are two notions of dimension that play complementary roles, so the emphasis on Hausdorff dimension will be replaced by the two: Hausdorff dimension and packing dimension. 6.1 will remain, but a new section on packing dimension will follow it, then the old sections 6.2--6.4 will be re-written to show both types of dimension; Substantial change in chapter 7: new examples along with recent developments; Sections rewritten to be made clearer and more focused.
Автор: Christoph Bandt; Kenneth Falconer; Martina Z?hle Название: Fractal Geometry and Stochastics V ISBN: 3319361570 ISBN-13(EAN): 9783319361574 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book collects significant contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five topical sections: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions.
Автор: Jose L. Encarnacao; Heinz-Otto Peitgen; Georgios S Название: Fractal Geometry and Computer Graphics ISBN: 3540553177 ISBN-13(EAN): 9783540553175 Издательство: Springer Рейтинг: Цена: 18167.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The aim of these conference papers was to present the wide spectrum of inter-relationships and interactions between fractal geometry and computer graphics. Topics discussed include computer graphics and optical simulation, image processing, image analysis and the simulation of natural phenomena.
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