Bounded and Divergent Trajectories And Expanding Curves on Homogeneous Spaces

Osama Khalil

Suppose $g_t$ is a $1$-parameter $\mathrm{Ad}$-diagonalizable subgroup of a Lie group $G$ and $\Gamma <G$ is a lattice. We study the dimension of bounded and divergent orbits of $g_t$ e…