Abstract

A symmetric Cantor set Kpq in [0, 1] with double fixed points 0 and 1 and contraction ratios p and q is called twofold Cantor set if it satisfies special exact overlap condition. We prove that all twofold Cantor sets have isomorphic self-similar structures and do not have weak separation property and that for Lebesgue-almost all (p, q) ∈ [0, 1/16]2 the sets Kpq are twofold Cantor sets.

Original languageEnglish
Pages (from-to)801-814
Number of pages14
JournalSiberian Electronic Mathematical Reports
Volume15
DOIs
Publication statusPublished - 1 Jan 2018

Keywords

  • Hausdorff dimension
  • Self-similar set
  • Twofold Cantor set
  • Weak separation property
  • HAUSDORFF DIMENSION
  • FRACTALS
  • self-similar set
  • SELF-SIMILAR SETS
  • SYSTEMS
  • weak separation property
  • twofold Cantor set

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