Weighted Badly Approximable Vectors and Games. (7th July 2017)

• Record Type: Journal Article
• Authors: Guan, Lifan; Yu, Jun
• Is Part Of: International mathematics research notices. Volume 2019:Number 3(2019)
• Page Start: 810
• Page End: 833
• Publication Date: 2017-07-07
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnx150
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: Let $d\ge 2$ . We show that the set ${\mathbf{Bad}}({\mathbf{r}})$ of ${\mathbf{r}}$ -badly approximable vectors in $\mathbb{R}^{d}$ is hyperplane absolute winning, hence is $1/2$ -winning for certain one-dimensional family of weights ${\mathbf{r}}$ .