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Patterns in thick compact sets
Israel Journal of Mathematics ( IF 1 ) Pub Date : 2021-07-02 , DOI: 10.1007/s11856-021-2173-6
Alexia Yavicoli 1
Affiliation  

We introduce a connection between Newhouse thickness and patterns through a variant of Schmidt’s game introduced by Broderick, Fishman and Simmons. This yields an explicit, robust and checkable condition that ensures that a Cantor set in the real line contains long arithmetic progressions and, more generally, homothetic copies of large finite sets.



中文翻译:

密集的紧凑集模式

我们通过 Broderick、Fishman 和 Simmons 引入的 Schmidt 游戏变体介绍了 Newhouse 厚度和模式之间的联系。这产生了一个明确的、鲁棒的和可检查的条件,确保实数行中的康托尔集包含长的算术级数,更一般地,包含大型有限集的同位副本。

更新日期:2021-07-04
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