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

Abstract

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

arXiv comment18 pages

References in corpus (4)

• The set of badly approximable vectors is strongly $C^1$ incompressible
• Badly approximable points on manifolds
• Badziahin-Pollington-Velani's theorem and Schmidt's game
• Weighted badly approximable vectors and games