Modul:   MAT760  Ergodic Theory and Dynamical Systems Seminar

Divergent on average trajectories for higher rank actions

Vortrag von Wooyeon Kim

Datum: 31.10.22  Zeit: 13.30 - 14.30  Raum: Y27H28

Let \(A\) be the group of positive diagonal \(d\times d\) matrices on \(SL_d(\mathbb{R})\) and \(U\cong \mathbb{R}^{d-1}\) be an abelian expanding horospherical group in \(SL_d(\mathbb{R})\), where \(d\ge 2\). Denote by \(A^{+}\) the expanding cone in \(A\) associated to \(U\). We say that \(x\in SL_d(\mathbb{R})/SL_d(\mathbb{Z})\) is \(A^{+}\)-divergent on average if for any compact set \(K\) the orbit \(A^{+}x\) escapes \(K\) on average. One may ask how large the set of points which are \(A^{+}\)-divergent on average is. In this talk, I will discuss upper and lower bounds for the Hausdorff dimension of the set of points which are \(A^{+}\)-divergent on average.