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

2018/11/22 by Abrosimov, Nikolai, Chanchieva, Marina, Tetenov, Andrey
#28A80 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1811.09219

Abstract

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

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