English

Products of two Cantor sets

Dynamical Systems 2017-04-26 v2

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.

Keywords

Cite

@article{arxiv.1601.01370,
  title  = {Products of two Cantor sets},
  author = {Yuki Takahashi},
  journal= {arXiv preprint arXiv:1601.01370},
  year   = {2017}
}

Comments

23 pages, 2 figures

R2 v1 2026-06-22T12:24:24.048Z