Fractal Geometry, Complex Dimensions and Zeta Functions Geometry and Spectra of Fractal Strings /

• Κύριοι συγγραφείς: Lapidus, Michel L. (Συγγραφέας), Frankenhuijsen, Machiel van (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York, 2006.
• Σειρά: Springer Monographs in Mathematics,
• Θέματα: Mathematics.; Dynamics.; Ergodic theory.; Global analysis (Mathematics).; Manifolds (Mathematics).; Measure theory.; Partial differential equations.; Number theory.; Topology.; Number Theory.; Measure and Integration.; Partial Differential Equations.; Dynamical Systems and Ergodic Theory.; Global Analysis and Analysis on Manifolds.

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...

Πίνακας περιεχομένων:

• 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.