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

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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. Key Features The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Lapidus, Michel L. (Autor), van Frankenhuijsen, Machiel (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer New York : Imprint: Springer, 2006.
Edición:1st ed. 2006.
Colección:Springer Monographs in Mathematics,
Temas:
Topology.
Number theory.
Measure theory.
Differential equations.
Dynamical systems.
Global analysis (Mathematics).
Manifolds (Mathematics).
Number Theory.
Measure and Integration.
Differential Equations.
Dynamical Systems.
Global Analysis and Analysis on Manifolds.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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