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 …

Let 9m be a finite set (called symbols) with the discrete topology and H= 9m be the set all
doubly infinite sequences of symbols with the product topology. In symbolic dynamics one …

Let φ be an Axiom A flow restricted to a basic set, let g be a C∞ function and let, where λg (τ)
is the g length of the closest orbit τ, λ (τ) is the period of τ and h is the topological entropy of …

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 …

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 …

Geodesic flows and interval maps are two topics in the theory of dynamical systems with a
long mathematical history. The first of these seems to have originated with Jacobi who …

Let (where t ε ℝ) and let μ be the G-invariant probability measure on G/Γ. We show that if x is
a non-periodic point of the flow given by the (ut)-action on G/Γ then the (ut)-orbit of 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 …

In this paper we shall exhibit a striking contrast in the ergodic behavior of two classical
dynamical systems: the geodesic and the horocycle flows on the unit tangent bundle of a …

Axiom A systems were originally introduced by Smale in his seminal paper on dynamical
systems [28]. One of their main purposes was to generalise Anosov systems (both …