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