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Published in:
2013 | OriginalPaper | Chapter
Complex Dimensions of Ordinary Fractal Strings
Authors : Michel L. Lapidus, Machiel van Frankenhuijsen
Published in: Fractal Geometry, Complex Dimensions and Zeta Functions
Publisher: Springer New York
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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 fractal sprays, which are a higher-dimensional analogue of fractal strings.