Complex Dimensions of Ordinary Fractal Strings

Michel L. Lapidus () and Machiel van Frankenhuysen ()
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Michel L. Lapidus: University of California, Department of Mathematics
Machiel van Frankenhuysen: University of California, Department of Mathematics

Chapter 1 in Fractal Geometry and Number Theory, 2000, pp 7-22 from Springer

Abstract: Abstract In this chapter, we recall some basic definitions pertaining to the notion of (ordinary) fractal string and introduce several new ones, the most important of which is the notion of complex dimension. We also give a brief overview of some of our results in this context by discussing the simple but illustrative example of the Cantor string. In the last section, we discuss the notion of fractal spray, which is a higher-dimensional analogue of that of fractal string.

Date: 2000
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DOI: 10.1007/978-1-4612-5314-3_2

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