Bounded orbits of diagonalizable flows on ${\mathrm{SL}}_3(\mathbb{R})/{\mathrm{SL}}_3(\mathbb{Z})$

Jinpeng An, Lifan Guan, Dmitry Kleinbock

We prove that for any countably many one-parameter diagonalizable subgroups $F_n$ of ${\mathrm{SL}}_3(\mathbb{R})$, the set of $\Lambda \in {\mathrm{SL}}_3(\mathbb{R})/{\mathrm{SL}}_3(\mathbb{Z})$ such that…