|M.Sc Student||Hemo Tamir|
|Subject||Homogeneous Asymptotic Limits of Uniform Averages on|
|Department||Department of Mathematics||Supervisor||PROF. Amos Nevo|
|Full Thesis text|
We study the distribution of matrix elements of discrete subgroups of the group of 2x2 unimodular matrices over the field of real numbers. Prominent examples are finitely generated subgroups of the group of 2x2 integral matrices.
For a non-elementary, geometrically finite group with critical exponent larger than 1/2, we demonstrate the equidistribution of homogeneous averages on the group taken in finite dimensional representations of the group of 2x2 unimodular matrices over the real numbers. The limit measure is given explicitly in terms of the representation and the Patterson-Sullivan measure corresponding to the discrete group.