2023/11/01 by Johanna Bimmermann, Bimmermann, Johanna
Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2311.00467
openalex publication_date 2023/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We compute the Hofer-Zehnder capacity of magnetic disc tangent bundles over constant curvature surfaces. We use the fact that the magnetic geodesic flow is totally periodic and can be reparametrized to obtain a Hamiltonian circle action. The oscillation of the Hamiltonian generating the circle action immediately yields a lower bound of the Hofer-Zehnder capacity. The upper bound is obtained from Lu's bounds of the Hofer-Zehnder capacity using the theory of pseudo-holomorphic curves. In our case the gradient spheres of the Hamiltonian will give rise to the non-vanishing Gromov-Witten invariant needed.