DCDS
Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology
Fernando Alcalde Cuesta Françoise Dal'Bo Matilde Martínez Alberto Verjovsky
We consider a minimal compact lamination by hyperbolic surfaces. We prove that if no leaf is simply connected, then the horocycle flow on its unitary tangent bundle is minimal.
keywords: geometrically infinite surfaces minimality. hyperbolic laminations horocycle flows Hyperbolic surfaces
JMD
Horocycle flows for laminations by hyperbolic Riemann surfaces and Hedlund's theorem
Matilde Martínez Shigenori Matsumoto Alberto Verjovsky
We study the dynamics of the geodesic and horocycle flows of the unit tangent bundle $(\hat M, T^1\mathfrak{F})$ of a compact minimal lamination $(M,\mathfrak{F})$ 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 $\mathfrak{F}$ has a leaf which is not simply connected, the horocyle flow is topologically transitive.
keywords: Hyperbolic surfaces horocycle and geodesic flows hyperbolic laminations minimality.
DCDS
Corrigendum to "Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology"
FERNANDO ALCALDE CUESTA Françoise Dal'Bo Matilde Martínez Alberto Verjovsky
keywords: Hyperbolic surfaces horocycle flows foliations

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