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

Show other versions (1)

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...

Full description

Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Lapidus, Michel L. (Author), van Frankenhuijsen, Machiel (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: New York, NY : Springer New York : Imprint: Springer, 2006.
Edition:1st ed. 2006.
Series:Springer Monographs in Mathematics,
Subjects:
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.
Online Access:Texto Completo
Table of Contents:
  • 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.

Similar Items