Fractal Geometry, Complex Dimensions and Zeta Functions

Geometry and Spectra of Fractal Strings


ISBN: 978-1-4614-2175-7 (Print) 978-1-4614-2176-4 (Online)

Table of contents (13 chapters)

  1. Front Matter

    Pages i-xxvi

  2. Chapter

    Pages 9-32

    Complex Dimensions of Ordinary Fractal Strings

  3. Chapter

    Pages 33-63

    Complex Dimensions of Self-Similar Fractal Strings

  4. Chapter

    Pages 65-117

    Complex Dimensions of Nonlattice Self-Similar Strings: Quasiperiodic Patterns and Diophantine Approximation

  5. Chapter

    Pages 119-135

    Generalized Fractal Strings Viewed as Measures

  6. Chapter

    Pages 137-178

    Explicit Formulas for Generalized Fractal Strings

  7. Chapter

    Pages 179-212

    The Geometry and the Spectrum of Fractal Strings

  8. Chapter

    Pages 213-235

    Periodic Orbits of Self-Similar Flows

  9. Chapter

    Pages 237-270

    Fractal Tube Formulas

  10. Chapter

    Pages 271-281

    Riemann Hypothesis and Inverse Spectral Problems

  11. Chapter

    Pages 283-295

    Generalized Cantor Strings and their Oscillations

  12. Chapter

    Pages 297-332

    Critical Zeros of Zeta Functions

  13. Chapter

    Pages 333-371

    Fractality and Complex Dimensions

  14. Chapter

    Pages 373-483

    New Results and Perspectives

  15. Back Matter

    Pages 485-567