Horocycle flows for laminations by hyperbolic Riemann surfaces and Hedlund's theorem

Abstract

We study the dynamics of the geodesic and horocycle flows of the unit tangent bundle $(\hat{M},T^1\mathcal{F})$ of a compact minimal lamination $(M,\mathcal{F})$ by negatively curved surfaces. We give conditions under which the action of the affine group generated by the joint action of these flows is minimal, and examples where this action is not minimal. In the first case, we prove that if $\mathcal{F}$ has a leaf which is not simply connected, the horocyle flow is topologically transitive.

Corrected version of previous paper "Hedlund's theorem for compact minimal laminations"

References in corpus (1)

• A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces

Cited by in corpus (5)

• Statistical Behaviour of the Leaves of Riccati Foliations
• Remarks on the horocycle flows for foliations by hyperbolic surfaces
• Weak form of equidistribution theorem for harmonic measures of foliations by hyperbolic surfaces
• On the construction of minimal foliations by hyperbolic surfaces on 3-manifolds
• The dichotomy of harmonic measures of compact hyperbolic laminations