Dimension drop for diagonalizable flows on homogeneous spaces

Dmitry Kleinbock, Shahriar Mirzadeh

Let $X=G/\Gamma$, where $G$ is a Lie group and $\Gamma$ is a lattice in $G$, let $O$ be an open subset of $X$, and let $F=\{g_t:t\ge 0\}$ be a one-parameter subsemigroup of $G$. Conside…