Fractality, Self-Similarity and Complex Dimensions
数论
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0401156,
title = {Fractality, Self-Similarity and Complex Dimensions},
author = {Michel L. Lapidus and Machiel van Frankenhuijsen},
journal= {arXiv preprint arXiv:math/0401156},
year = {2007}
}
备注
To appear in Proceedings of Symposia of Pure Mathematics, title: "Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot"