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 …

Given an actionof a groupG, say, on a locally compact Hausdorff space X (namely, a
dynamical system) one would like to understand the closures of the individual orbits and, in …

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 …

By the classical result of Hopf [12], the geodesic flow on a surface of constant negative
curvature and finite area is ergodic. In the case of a compact surface the flow has …

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 …

Geodesic and Horocyclic Trajectories presents an introduction to the topological dynamics
of two classical flows associated with surfaces of curvature− 1, namely the geodesic and …

1. Introduction. Geodesic systems, particularly those on twodimensional manifolds, have
been a rich source in the determination and display of the possible types of macroscopic …

Indeed, Margulis [lo] announced that for the geodesic flow on a d-dimensional compact
manifold of curvature-1 the number of periodic orbits 7 with (minimal) period r (1) I x is …

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 …

Factors of horocycle flows Page 1 Ergod. Th. & Dynam. Sys. (1982), 2, 465-489 Printed in Great
Britain Factors of horocycle flows MARINA RATNER Department of Mathematics, University of …