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

Nastaran Einabadi

We prove that a generic element of the Anosov-Katok class of the torus, ${\overline{\mathcal{O}}}^{\infty }({\mathbb{T}}^2)$, acts parabolically and non-properly on the fine curve graph…