Iterated Function Systems in Mixed Euclidean and p-adic Spaces

Details Iterated Function Systems in Mixed Euclidean and p-adic Spaces Iterated Function Systems in Mixed Euclidean and p-adic Spaces

2006-10-23

arxiv.org/abs/math/0610687v1

In: M.M. Novak (ed.), Complexus Mundi - Emergent Patterns in Nature, World Scientific, Singapore (2006), pp. 267-276.

Mathematics

Metric Geometry

10 pages, 2 Figures; Proceedings of the Conference "Fractal 2006" held in Vienna, Austria, from February 12 to February 15, 20

Scientific paper

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.

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