Fractality, SelfSimilarity and Complex Dimensions
Abstract
We present an overview of a theory of complex dimensions of selfsimilar 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2004
 arXiv:
 arXiv:math/0401156
 Bibcode:
 2004math......1156L
 Keywords:

 Mathematics  Number Theory;
 Primary 11M41;
 28A80;
 Secondary 11G20;
 11J70
 EPrint:
 To appear in Proceedings of Symposia of Pure Mathematics, title: "Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot"