Bounded orbits of certain diagonalizable flows on $S{L}_n(\mathbb{R})/S{L}_n(\mathbb{Z})$

Lifan Guan, Weisheng Wu

We prove that the set of points that have bounded orbits under certain diagonalizable flows is a hyperplane absolute winning subset of $S{L}_n(\mathbb{R})/S{L}_n(\mathbb{Z})$.