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

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

2006-07-31

arxiv.org/abs/math/0608002v1

Mathematics

Dynamical Systems

25 pages, to appear in Ergodic Theory and Dynamical Systems

Scientific paper

In 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.

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