Hausdorff dimension of the set of points on divergent trajectories of a homogeneous flow on a product space

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115226In this paper we compute the Hausdorff dimension of the set D_n of points on divergent trajectories of the homogeneous flow induced by a certain one-parameter subgroup of G=SL(2,R) acting by left multiplication on the product space G^n/Gamma^n, where Gamma=SL(2,Z). We prove that the Hausdorff dimension of D_n equals 3n-(1/2) for any n greater than one.25 pages, to appear in Ergodic Theory and Dynamical SystemsDynamical SystemsMathematical Physics37A17; 11K40; 22E40; 11J70; 82C40Hausdorff dimension of the set of points on divergent trajectories of a homogeneous flow on a product spacetext