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 …

Publisher Summary This chapter focuses on the discrete subgroups and the ergodic theory.
It presents the formulation of results and conjectures. The results on the behavior of …

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 …

We show that if G is a semisimple algebraic group defined over Q and Γ is an arithmetic
lattice in G:= GR with respect to the Q-structure, then there exists a compact subset C of G/Γ …

1. Let B be a real nondegenerate indefinite quadratic form in n variables-It is well known that
if n 2 5 and the coefficients of B are rational then B represents zero nontrivially, ie there exist …

We show that if (ut) is a one-parameter subgroup of SL (n, ℝ) consisting of unipotent
matrices, then for any ε> 0 there exists a compact subset K of SL (n, ℝ)/SL (n, ℤ) such that …

In this paper we discuss the use of dynamical and ergodic-theoretic ideas and methods to
solve some long-standing problems originating from Lie groups and number theory. These …

Let B be a real nondegenerate indefinite quadratic form on E", where n> 3, which is not a
multiple of a rational form (that is, B is not of the form tB o where te E and B oa quadratic form …

This volume is devoted to the" hyperbolic theory" of dynamical systems (DS), that is, the
theory of smooth DS's with hyperbolic behaviour of the tra jectories (generally speaking, not …

We construct canonical positive currents and heights on the boundary of the ample cone of a
K3 surface. These are equivariant for the automorphism group and fit together into a …