Dynamics of Kleinian groups and applications

par Athmane Hachim

vendredi 29 nov. 2024, 10:30 → 11:30 Europe/Paris

207 (Bat 1R2)

In this talk, we present our recent work on the dynamics of a Kleinian group $\mathrm{\Gamma }$ acting on the tangent bundle $T{\mathbb{CP}}^1$. Similar to the dynamics of $\mathrm{\Gamma }$ on ${\mathbb{CP}}^1$, the action of $\mathrm{\Gamma }$ on $T{\mathbb{CP}}^1$ partitions the space into a discontinuous part and a "recurrent" part lying above the limit set of $\mathrm{\Gamma }$ in ${\mathbb{CP}}^1$. We explore the dynamics of $\mathrm{\Gamma }$ on this recurrent part, with a focus on the case where $\mathrm{\Gamma }$ contains a parabolic element. Additionally, we discuss the motivations behind these investigations and their applications, particularly in describing the dynamics of generalized semicomplete Halphen vector fields.