Fractality, Self-Similarity and Complex Dimensions
arXiv:math/0401156
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.
To appear in Proceedings of Symposia of Pure Mathematics, title: "Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot"