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Fractality, Self-Similarity and Complex Dimensions

Michel L. Lapidus·Machiel van Frankenhuijsen
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Abstract

We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several strands to discuss a possible approach to establishing a cohomological interpretation of the complex dimensions.

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Michel L. Lapidus, Machiel van Frankenhuijsen. 2004-01-14. Fractality, Self-Similarity and Complex Dimensions. https://arxiv.org/abs/math/0401156

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