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Fractal Geometry, Complex Dimensions and Zeta Functions

Geometry and Spectra of Fractal Strings
BuchGebunden
452 Seiten
Englisch
Springererschienen am12.09.2006
Number theory, spectral geometry, and fractal geometry are interlinked in this study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. The Riemann hypothesis is given a natural geometric reformulation in context of vibrating fractal strings, and the book offers explicit formulas extended to apply to the geometric, spectral and dynamic zeta functions associated with a fractal.mehr
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EUR71,64
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Produkt

KlappentextNumber theory, spectral geometry, and fractal geometry are interlinked in this study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. The Riemann hypothesis is given a natural geometric reformulation in context of vibrating fractal strings, and the book offers explicit formulas extended to apply to the geometric, spectral and dynamic zeta functions associated with a fractal.
Details
ISBN/GTIN978-0-387-33285-7
ProduktartBuch
EinbandartGebunden
Verlag
Erscheinungsjahr2006
Erscheinungsdatum12.09.2006
ReiheSpringer Monographs in Mathematics
Reihen-Nr.Mathematics
Seiten452 Seiten
SpracheEnglisch
Gewicht808 g
Illustrationenw. 53 figs.
Artikel-Nr.10713684

Inhalt/Kritik

Inhaltsverzeichnis
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.mehr