4 papers · 1 filter
On the non-expansiveness of the geodesic flow on surfaces with cusps
Sergi Burniol Clotet, Françoise Dal'Bo
We exhibit orbits of the geodesic flow on a hyperbolic surface with at least one cusp such that every tubular neighborhood contains uncountably many distinct geodesic flow orbits.…
Bellis strong stable sets on infinite hyperbolic surfaces
Sergi Burniol Clotet, Françoise Dal'Bo, Sergio Herrero Vila
We provide a corrected proof of a theorem of A. Bellis on strong stable sets in the unit tangent bundle of certain hyperbolic surfaces. The theorem states that, for vectors whose g…
Weaving Geodesics and New Phenomena in Horocyclic Dynamics
Françoise Dal'bo, James Farre, Or Landesberg +1
We construct geometrically infinite hyperbolic surfaces supporting horocycles with tailored recurrence properties. In particular, we obtain the first examples of non-trivial minima…
Unique ergodicity of the horocycle flow on Riemannnian foliations
Fernando Alcalde Cuesta, Françoise Dal'Bo, Matilde Martínez +1
A classic result due to Furstenberg is the strict ergodicity of the horocycle flow for a compact hyperbolic surface. Strict ergodicity is unique ergodicity with respect to a measur…