In this paper we study the behavior of the closed orbits of the classical horocycle flow, on the
space of linear elements of a Riemann surface carrying the Poincari metric. Call the surface …

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 …

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 …

In this paper we investigate the relationship between two topics which at first sight seem
unrelated. The first deals with ergodic properties of geodesic flows on two-dimensional …

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 class of all invariant measures of a transformation, or a flow, is an important aspect of its
dynamics. Thus for instance if T is a homeomorphism of a locally compact space X then any …

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 …

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 …

We consider Reeb flows on the tight 3-sphere admitting a pair of closed orbits forming a
Hopf link. If the rotation numbers associated to the transverse linearized dynamics at these …

We give effective bounds on the deviation of ergodic averages for the horocycle flow on the
unit tangent bundle of a noncompact hyperbolic surface of finite area. The bounds depend …