Weighted Badly Approximable Vectors and Games. (7th July 2017) - Guan, Lifan
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 ${\mathbf{r}}$ .