Iterated Function Systems in Mixed Euclidean and p-adic Spaces
arXiv:math/0610687 · doi:10.1142/9789812774217_0024
Abstract
We investigate graph-directed iterated function systems in mixed Euclidean and p-adic spaces. Hausdorff measure and Hausdorff dimension in such spaces are defined, and an upper bound for the Hausdorff dimension is obtained. The relation between the Haar measure and the Hausdorff measure is clarified. Finally, we discus an example in ${Bbb R}\times{\Bbb Q}\sb 2$ and calculate upper and lower bounds for its Hausdorff dimension.
10 pages, 2 Figures; Proceedings of the Conference "Fractal 2006" held in Vienna, Austria, from February 12 to February 15, 2006