We present a new approach to metric Diophantine approximation on manifolds based on the
correspondence between approximation properties of numbers and orbit properties of …

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 …

Unipotent Flows and Counting Lattice Points on Homogeneous Varieties Page 1 Annals of
Mathematics, 143 (1996), 253-299 Unipotent flows and counting lattice points on homogeneous …

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 …

The earthquake flow and the Teichmüller horocycle flow are flows on bundles over the
Riemann moduli space of a surface, and are similar in many respects to unipotent flows on …

Soit S une variete de Shimura sur C. On definit sur S un ensemble de points speciaux (les
points a multiplication complexe) et un ensemble de sous-varietes speciales que l'on …

This survey paper is not a complete reference guide to number-theoretical applications of
ergodic theory. Instead, it considers an approach to a class of problems involving …

Abstract Let U:= L\G be a homogeneous variety defined over a number field K, where G is a
connected semisimple K-group and L is a connected maximal semisimple K-subgroup of G …

Applications du thunhbox voidb@x group let unhbox voidb@x setbox @tempboxa hbox {eglobal
mathchardef accent@spacefactor spacefa Page 1 COMPOSITIO MATHEMATICA Compositio …