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

Amadou Sy

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arXiv · 2510.20464

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

Amadou Sy

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Abstract

The aim of this article is to show that if there exists $u \in \Omega_{h} \subset T^{1}S$ an infinite quasi-minimizing ray which do not intersect any closed geodesic on the surface $S$ (untwisted flute), then $T_{u}=\{ t \in \mathbb{R} \; ; \; g_{t}u \in \overline{h_{\mathbb{R}}u} \}=\{0\}$.

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Amadou Sy. 2025-10-23. Recurrent and irregular orbits of the horocyclic flow on the unit tangent bundle of the untwisted flute. https://arxiv.org/abs/2510.20464

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