English

On the set of subarcs in some non-postrcritically finite dendrites

Metric Geometry 2018-12-21 v2

Abstract

We construct a family of non-PCF dendrites KK in a plane, such that in each of them all subarcs have the same Hausdorff dimension ss, while the set of ss-dimensional Hausdorff measures of subarcs connecting the given point and a self-similar Cantor subset in K is a Cantor discontinuum.

Keywords

Cite

@article{arxiv.1811.09219,
  title  = {On the set of subarcs in some non-postrcritically finite dendrites},
  author = {Nikolai Abrosimov and Marina Chanchieva and Andrey Tetenov},
  journal= {arXiv preprint arXiv:1811.09219},
  year   = {2018}
}