Abstract
In this article, we introduce a notion of size for sets, called the thickness, that can be used to guarantee that two Cantor sets intersect (the Gap Lemma) and show a connection among thickness, Schmidt games and patterns. We work mostly in the real line, but we also introduce the topic in higher dimensions.
Subject
Applied Mathematics,Computational Mathematics,General Engineering
Reference29 articles.
1. Newhouse, S.E. (1970). Global Analysis, American Mathematical Society.
2. The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms;Newhouse;Inst. Hautes Études Sci. Publ. Math.,1979
3. Cantor sets and numbers with restricted partial quotients;Astels;Trans. Am. Math. Soc.,2000
4. Boone, Z., and Palsson, E.A. (2022). A pinned Mattila–Sjölin type theorem for product sets. arXiv.
5. Intersections of thick compact sets in ℝd;Falconer;Math. Z.,2022
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. A Survey on the Hausdorff Dimension of Intersections;Mathematical and Computational Applications;2023-03-22