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Complex Dimensions of Self-Similar Fractal Strings

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

An important class of examples of ordinary fractal strings is provided by the so-called self-similar strings, which we will use throughout this book to illustrate our theory. These are constructed in the usual way with the aid of contraction mappings. In this chapter, we give a detailed analysis of the structure of the complex dimensions of such fractal strings.

Suggested Citation

  • Michel L. Lapidus & Machiel van Frankenhuysen, 2000. "Complex Dimensions of Self-Similar Fractal Strings," Springer Books, in: Fractal Geometry and Number Theory, chapter 2, pages 23-54, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-5314-3_3
    DOI: 10.1007/978-1-4612-5314-3_3
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