Iterated Function Systems in Mixed Euclidean and p-adic Spaces

Bernd Sing

doi:10.1142/9789812774217_0024

Iterated Function Systems in Mixed Euclidean and p-adic Spaces

度量几何 2019-07-23 v1

作者: Bernd Sing

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摘要

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.

关键词

hausdorff dimension assouad dimension hausdorff measure and dimension

引用

@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}
}

备注

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

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