2004/01/14 by Michel L. Lapidus, Lapidus, Michel L., Machiel van Frankenhuijsen +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #11J70 #28A80 #Complex Systems and Time Series Analysis #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Primary 11M41 #Secondary 11G20 #math.NT #msc:11G20 #msc:11J70 #msc:11M41 #msc:28A80
paper · pdf · doi:10.48550/arxiv.math/0401156
To appear in Proceedings of Symposia of Pure Mathematics, title: "Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot"
arxiv created 2004/01/14 · openalex publication_date 2004/01/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.