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

2024/05/29 by Nastaran Einabadi, Einabadi, Nastaran
#math.DS #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.2405.19123

Abstract

We prove that a generic element of the Anosov-Katok class of the torus, O^∞(\mathbbT²), acts parabolically and non-properly on the fine curve graph C^†(\mathbbT²). Additionally, we show that a generic element of O^∞(\mathbbT²) admits generalized rotation sets of any point-symmetric compact convex homothety type in the plane.

Related

• Parabolic isometries of the fine curve graph of the torus
• Parabolic isometries of the fine curve graph of the torus
• Rotation sets and axes in the fine curve graph for torus homeomorphisms
• On the rotation sets of generic homeomorphisms on the torus
• Generic Rotation Sets in Hyperbolic Surfaces