Lapidus Michel L., Frankenhuijsen Machiel van Fractal Geometry, Complex Dimensions and Zeta Functions / Geometry and Spectra of Fractal Strings 9780387332857

Варианты приобретения

Цена: 7400.00р.
Кол-во:
о цене
Наличие: Отсутствует. Возможна поставка под заказ.

При оформлении заказа до: 2025-07-28
Ориентировочная дата поставки: Август-начало Сентября
При условии наличия книги у поставщика.

Добавить в корзину

в Мои желания

Автор: Lapidus Michel L., Frankenhuijsen Machiel van
Название: Fractal Geometry, Complex Dimensions and Zeta Functions / Geometry and Spectra of Fractal Strings
Перевод названия: Рекурсивная геометрия, сложные измерения и дзэта функции
ISBN: 9780387332857
Издательство: Springer
Классификация:

Математика

Основы высшей математики и математический анализ

Топология

Прикладная математика

ISBN-10: 0387332855
Обложка/Формат: Hardback
Страницы: 488
Вес: 0.80 кг.
Дата издания: 12.09.2006
Серия: Springer Monographs in Mathematics
Язык: English
Иллюстрации: 54 black & white illustrations, 54 black & white line drawings
Размер: 23.57 x 16.31 x 2.69 cm
Читательская аудитория: Undergraduate
Подзаголовок: Geometry and spectra of fractal strings
Ссылка на Издательство: Link
Рейтинг:
Поставляется из: Германии
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.
Дополнительное описание: Формат: 235x155
Илюстрации: 54
Круг читателей: Graduate students, geometers, math physicists, number theorists
Ключевые слова:
Язык: eng
Оглавление: List of Figures.- Preface.- Overview.- Introduction.- Complex Dimensions of Ordinary Fractal Strings.- Complex Dimensions of Self-Similar Fractal Strings.- Complex Dimensions of Nonlattice Self-Similar Strings: Quasiperiodic Patterns and Diophantine Approximation.- Generalized Fractal Strings Viewed as Measures.- Explicit Formulas for Generalized Fractal Strings.- The Geometry and the Spectrum of Fractal Strings.- Periodic Orbits of Self-Similar Flows.- Tubular Neighborhoods and Minkowski Measurability.- The Riemann Hypothesis and Inverse Spectral Problems.- Generalized Cantor Strings and their Oscillations.- The Critical Zeros of Zeta Functions.- Concluding Comments, Open Problems, and Perspectives.- Appendices.- A. Zeta Functions in Number Theory.- B. Zeta Functions of Laplacians and Spectral Asymptotics.- C. An Application of Nevanlinna Theory.- Bibliography.- Acknolwedgements.- Conventions.- Index of Symbols.- Author Index.- Subject Index.

Fractal Geometry, Complex Dimensions and Zeta Functions / Geometry and Spectra of Fractal Strings, Lapidus Michel L., Frankenhuijsen Machiel van