English

Iterated Function Systems in Mixed Euclidean and p-adic Spaces

Metric Geometry 2019-07-23 v1

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 BbbR×Q\sb2{Bbb R}\times{\Bbb Q}\sb 2 and calculate upper and lower bounds for its Hausdorff dimension.

Keywords

Cite

@article{arxiv.math/0610687,
  title  = {Iterated Function Systems in Mixed Euclidean and p-adic Spaces},
  author = {Bernd Sing},
  journal= {arXiv preprint arXiv:math/0610687},
  year   = {2019}
}

Comments

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