Dynamics & probability: Omri Solan (TAU) - Divergent trajectories in SL_3(R)/SL_3(Z)

Tue, 15/12/201514:00-16:30
Manchester building, Hebrew University of Jerusalem, 209
It is well known that the diophantine-approximation concept of singular vectors is related to the dynamical object of divergent g-trajectories, for g(t)=diag(e^t, e^t, e^{-2t}). Cheung (2007) provides an exact formula for the Hausdorff dimension of the set of divergent g-trajectories starting at an H-orbit, where H is the expanding horospherical subgroup associated to g, and thereby obtains a similar formula for the dimension of the set of singular vectors. We calculate the Hausdorff dimension of the analogous set when replacing the group g(t) by the group g'(t)=diag(e^{\xi_1 t}, e^{\xi_2 t}, e^{-t}), where \xi_1>\xi_2>0 and \xi_1+\xi_2=1, and keeping the group H.
The talk will not assume prior knowledge of the concepts mentioned above.