Bounded trajectories of quasi-rays on homogeneous spaces and Diophantine approximation with weight functions

Dmitry Kleinbock, Vasiliy Neckrasov

Let $G$ be a connected semisimple real Lie group, $\Gamma$ an irreducible lattice in $G$ and $X=G/\Gamma$. Let $F=\{g_t:t\ge 0\}$ be a non-quasiunipotent one-parameter subsemigroup of $…