|Jul 18, 2023
For d>2 let G=SL_d(R). Let A be the group of positive diagonal dtimes d matrices on G and U be a (d-1)-dimensional abelian expanding horospherical group in G. For a point x in the space of d-dimensional lattices, we say that x is A-divergent on average if for any compact set K the orbit Ax escapes K on average. In this talk, I will discuss the Hausdorff dimension of the set of A-divergent on average points on closed U-orbits. If time permits, I will also discuss an application to inhomogeneous multiplicative Diophantine approximation.