Recurrent and irregular orbits of the horocyclic flow on the unit tangent bundle of the untwisted flute

2025/10/23 by Amadou Sy, Sy, Amadou
Mathematics · #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2510.20464

Abstract

The aim of this article is to show that if there exists u ∈ Ω_h ⊂ T¹S an infinite quasi-minimizing ray which do not intersect any closed geodesic on the surface S (untwisted flute), then T_u=\ t ∈ ℝ ; g_tu ∈ h_ℝu \=\0\.

Citations

• On links between horocyclic and geodesic orbits on geometrically\n infinite surfaces
• Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology

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• Récurrence ou non minimalité des adhérences des d'orbites irréguliéres du flot horocyclique de finesse infinie
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• Ergodic Geodesic Flows and First Kind Flute Surfaces
• Weaving Geodesics and New Phenomena in Horocyclic Dynamics