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Introduction

In: Fractal Geometry and Number Theory

Author

Listed:
  • Michel L. Lapidus

    (University of California, Department of Mathematics)

  • Machiel van Frankenhuysen

    (University of California, Department of Mathematics)

Abstract

A fractal drum is a bounded open subset of ℝ m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geometry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex dimensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the references therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7.1, 10.3 and 10.4, along with Appendix B.)

Suggested Citation

  • Michel L. Lapidus & Machiel van Frankenhuysen, 2000. "Introduction," Springer Books, in: Fractal Geometry and Number Theory, pages 1-6, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-5314-3_1
    DOI: 10.1007/978-1-4612-5314-3_1
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