Séminaire de Géométrie et Topologie

Torus diffeomorphisms with parabolic and non-proper actions on the fine curve graph and their sublinear rotation sets

by Ms Nastaran Einabadi

Europe/Paris
1R2-207

1R2-207

Description
We prove that a generic element in the Anosov-Katok class of the torus $\overline{\mathcal{O}}^\infty(\mathbb{T}^2)$ acts parabolically and non-properly on the fine curve graph $\mathcal{C}^\dagger(\mathbb{T}^2)$. Additionally, we show that a generic element of $\overline{\mathcal{O}}^\infty(\mathbb{T}^2)$ admits sublinear rotation sets of all homothety types of non-empty point-symmetric compact convex subsets of the plane.