Fractal Geometry, Complex Dimensions and Zeta Functions Geometry and Spectra of Fractal Strings |
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| Author:
| Lapidus, Michel L.
Van Frankenhuysen, Machiel |
| Series title: | Springer Monographs in Mathematics |
| ISBN: | 978-0-387-33285-7 |
| Publication Date: | Jan 2006 |
| Publisher: | Springer
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| Book Format: | Hardback |
| List Price: | AUD $152.95 |
Book Description:
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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. In this book The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings. The book also offers explicit formulas extended to apply to the geometric, spectral, and dynamic zeta functions associated with a fractal. In addition, numerous theorems, examples,...
More DescriptionNumber 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. In this book The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings. The book also offers explicit formulas extended to apply to the geometric, spectral, and dynamic zeta functions associated with a fractal. In addition, numerous theorems, examples, remarks and illustrations enrich the text. Throughout the book 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. The book will further appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics.