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arXiv · 2405.19123

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

Nastaran Einabadi
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Abstract

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 $C^{\dagger}(\mathbb{T}^2)$. Additionally, we show that a generic element of $\overline{\mathcal{O}}^{\infty}(\mathbb{T}^2)$ admits generalized rotation sets of any point-symmetric compact convex homothety type in the plane.

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Nastaran Einabadi. 2024-05-29. Torus diffeomorphisms with parabolic and non-proper actions on the fine curve graph and their generalized rotation sets. https://doi.org/10.2140/gt.2026.30.1963

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