On \(\epsilon\)-escaping trajectories in homogeneous spaces (Q2229253)

Fix a connected semisimple Lie group \(G\), a connected simple Lie subgroup \(G_0\subset G\) and a lattice \(\Gamma\subset G\), and let \(\mathfrak g_0\) be the Lie algebra of \(G_0\). Then there is a positive constant \(c\) depending only on \(G\), \(G_0\) and \(\Gamma\) such that for all semisimple \(D\in\mathfrak g_0\) and \(\varepsilon\in(0,1]\) the Hausdorff codimension of the set of points of \(G_0\) that are sequentially \(\varepsilon\)-escaping on average with respect to \(\{\mbox{exp}(tD)\}\) is at least \(c\varepsilon\).