Yitwah Cheung (Northwestern University)

Hausdorff dimension of the set of divergent trajectories in a product space.

Abstract. Let $g_t=diag(\exp(t),\exp(-t))$ act by right multiplication in each factor of the product space $X=(H\backslash G)^n$ where $G=SL_2({\mathbb R})$ and $H=SL_2({\mathbb Z})$. Let D be the subset of X consisting of those points whose orbit under the action leaves every compact set. We show that the Hausdorff dimension of D is 3n-1/2.