Products of two Cantor sets

Yuki Takahashi

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

We consider products of two Cantor sets, and obtain the optimal estimates in terms of their thickness that guarantee that their product is an interval. This problem is motivated by the fact that the spectrum of the Labyrinth model, which is a two dimensional quasicrystal model, is given by a product of two Cantor sets. We also discuss the connection with the question on the structure of intersections of two Cantor sets which was considered by many authors previously.

Original languageEnglish
Pages (from-to)2114-2137
Number of pages24
JournalNonlinearity
Volume30
Issue number5
DOIs
Publication statusPublished - 2017 Apr 10

Keywords

  • Cantor set
  • fractal
  • stable intersection
  • thickness

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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