arXiv subjects

Amadou Sy

Publications and source records attributed to Amadou Sy.

3 recordsLinked to original sources

arXiv2025

R\'ecurrence ou non minimalit\'e des adh\'erences des d'orbites irr\'eguli\'eres du flot horocyclique de finesse infinie

The topological dynamics of the horocyclic flow $h_{\mathbb{R}}$ on the unit tangent bundle of a geometrically finite hyperbolic surface is well known. In particular, on such a surface, the flow $h_{\mathbb{R}}$ is minimal, or the minimal sets are the periodic orbits. When the surface is geometrically infinite, the situation is more complex, and the presence of possible non-closed and non-dense orbits, called irregular orbits, complicates the description of minimal sets. In this text, we will show that such an orbit is recurrent, or its closure is non-$h_{\mathbb{R}}$ minimal. This would allow us to almost complete the description of $h_{\mathbb{R}}$-minimal sets.

math.GT↗

arXiv2025

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

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 $T_{u}=\{ t \in \mathbb{R} \; ; \; g_{t}u \in \overline{h_{\mathbb{R}}u} \}=\{0\}$.

math.GT↗

arXiv2025

On the closure of irregular orbits of the horocyclic flow on infinite finness

The topological dynamics of the horocyclic flow h_R on the unit tangent bundle of a geometrically finite hyperbolic surface is well known. In particular on such a surface the flow h_R is minimal or the minimal sets are the periodic orbits. When the surface is geometrically infinite, the situation is more complex and the presence of possible irregular orbits makes the description of minimal sets complicated. In this text, we construct a family of infinite hyperbolic surfaces for which the horocyclic flow defined on the unit tangent bundle is not minimal.

math.DS↗