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

Nikolay Vladimirovich Abrosimov, Marina Vladimirovna Chanchieva, Andrey Viktorovich Tetenov

Research output: Contribution to journalArticlepeer-review

Abstract

We construct a family F of non-PCF dendrites K in a plane, such that for any dendrite K ∈ F all its 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.

Original languageEnglish
Pages (from-to)975-982
Number of pages8
JournalСибирские электронные математические известия
Volume16
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Hausdorff dimension
  • Postcritically finite set
  • Ramification point
  • Self-similar dendrite
  • postcritically finite set
  • self-similar dendrite
  • ramification point
  • SYSTEMS

OECD FOS+WOS

  • 1.01 MATHEMATICS

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