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: Feder Название: Fractals ISBN: 0306428512 ISBN-13(EAN): 9780306428517 Издательство: Springer Рейтинг: Цена: 20896.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This lovely little book will take off and fly on its own power, but the author has asked me to write a few words, and one should not say no to a friend.
Автор: Falconer Kenneth Название: Fractals: A Very Short Introduction ISBN: 0199675988 ISBN-13(EAN): 9780199675982 Издательство: Oxford Education Рейтинг: Цена: 1978.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: From the contours of coastlines to the outlines of clouds, fractal shapes can be found regularly in nature. This Very Short Introduction explains the basic concepts, presents the `new geometry` of fractals, explores its wide range of applications, and shows the central place fractals have gained in mathematics and science in recent years.
Автор: Feldman David P Название: Chaos and Fractals ISBN: 0199566445 ISBN-13(EAN): 9780199566440 Издательство: Oxford Academ Рейтинг: Цена: 6810.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: For students with a background in elementary algebra, this book provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia Sets and the Mandelbrot Set, power laws, and cellular automata. The book includes over 200 end-of-chapter exercises.
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.
Описание: Provides a comprehensive treatment of all the techniques in nonlinear dynamics together with C++, Java and SymbolicC++ implementations. This book not only covers the theoretical aspects of the topics but also provides the practical tools. To understand the material, it includes more than 100 worked out examples and 150 ready to run programs.
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