Fractality, Self-Similarity and Complex Dimensions

Details Fractality, Self-Similarity and Complex Dimensions Fractality, Self-Similarity and Complex Dimensions

2004-01-14

arxiv.org/abs/math/0401156v1

Mathematics

Number Theory

To appear in Proceedings of Symposia of Pure Mathematics, title: "Fractal Geometry and Applications: A Jubilee of Benoit Mande

Scientific paper

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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