arXiv subjects

Masseye Gaye

Publications and source records attributed to Masseye Gaye.

4 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

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↗

arXiv2022

Triangles, Fractales and Spaghetti

There is well-known problem of geometric probability which can be quote as the Broken Spaghetti Problem. It addresses the following question: A stick of spaghetti breaks into three parts and all points of the stick have the same probability to be a breaking point. What is the probability that the three sticks, putting together, form a triangle? In these notes, we describe a hidden geometric pattern behind the symmetric version of this problem, namely a fractal that parametrizes the sample space of this problem. Using that fractal, we address the question about the probability to obtain a $δ$-equilateral triangle.

math.HO↗

arXiv2021

Combinatorial $k$-systoles on a punctured torus and a pair of pants

In this paper, $S$ denotes a surface homeomorphic to a punctured torus or a pair of pants. Our interest is the study of \emph{\textbf{combinatorial $k$-systoles}} that is closed curves with self-intersection numbers greater than $k$ and with least combinatorial length. We show that the maximal intersection number $I^c_k$ of combinatorial $k$-systoles of $S$ grows like $k$ and $\underset{k\rightarrow+\infty}{\limsup}(I^c_k-k)=+\infty$. This result, in case of a pair of pants and a punctured torus, is a positive response to the combinatorial version of the Erlandsson - Parlier conjecture, originally formulated for the geometric length.

math.GT↗