We prove results about orbit closures and equidistribution for the SL (2, ℝ) action on the
moduli space of compact Riemann surfaces, which are analogous to the theory of unipotent …

We prove some ergodic-theoretic rigidity properties of the action of on moduli space. In
particular, we show that any ergodic measure invariant under the action of the upper …

The study of geodesic flows on homogeneous spaces is an area of research that has
recently yielded some fascinating developments. This book focuses on many of these, with …

Asymptotic formulas on flat surfaces Page 1 Ergod. Th. & Dynam. Sys. (2001), 21, 443–478
Printed in the United Kingdom c 2001 Cambridge University Press Asymptotic formulas on …

This paper represents part II in our three part series on Raghunathan's measure conjecture
(see [R4] for part I). More specifically, let G be a real Lie group (all groups in this paper are …

The goals of this paper are first to describe and then to apply an ergodictheoretic
generalization of the Siegel integral formula from the geometry of numbers. The general …

Let L be a Lie group and λ a lattice in L. Suppose G is a non-compact simple Lie group
realized as a Lie subgroup of L and GA= L. Let aεG be such that Ada is semisimple and not …

Publisher Summary This chapter presents an exposition of homogeneous dynamics—that is,
the dynamical and ergodic properties of actions on the homogeneous spaces of Lie groups …

For d-dimensional ellipsoids E with d≥ 5 we show that the number of lattice points in rE is
approximated by the volume of rE, as r tends to infinity, up to an error of order O(r^d-2) for …

Under explicit diophantine conditions on, we prove that the local two-point correlations of the
sequence given by the values, with (m, n)∈ Z2, are those of a Poisson process. This partly …