Recurrent and irregular orbits of the horocyclic flow on the unit tangent bundle of the untwisted flute
Abstract
The aim of this article is to show that if there exists u ∈ h ⊂ T1S an infinite quasi-minimizing ray which do not intersect any closed geodesic on the surface S (untwisted flute), then Tu=\ t ∈ R \; ; \; gtu ∈ hRu \=\0\.
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