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

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 …

A well-known class of flows arises as follows: Let G be a semisimple Lie group and F be a
lattice in G, that is, F is a discrete subgroup such that G/F admits a finite measure invariant …

The modern study of dynamical systems on homogeneous spaces has roots in classical
dynamics and classical number theory. For example, the geodesic flow on a surface of …

Let G be a connected Lie group and Γ be a lattice in G; that is, Γ is a discrete subgroup of G
such that G/Γ admits a finite G-invariant measure. Let {gt} teP be a oneparameter subgroup …

Introduction. Professor Hedlund's name is associated with two of the classical dynamical
systems of topological dynamics, the geodesic flow and the horocycle flow on surfaces of …

An important problem in ergodic theory is to determine when the restriction to a subgroup of
an ergodic action of a group is still ergodic. Classical results concerning the ergodicity of …

Let G be a connected Lie group and let Γ be a lattice in G (not necessarily co-compact). We
show that if (ut) is a unipotent one-parameter subgroup of G then every ergodic invariant …

Here is an introduction to dynamical systems and ergodic theory with an emphasis on
smooth actions of noncompact Lie groups. The main goal is to serve as an entry into the …