Magnetic billiards and the Hofer-Zehnder capacity of disk tangent bundles of lens spaces

2024/03/11 by Johanna Bimmermann, Bimmermann, Johanna, Levin Maier +1 · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2403.06761

openalex publication_date 2024/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the Hofer-Zehnder capacity of disk tangent bundles of certain lens spaces with respect to the round metric. Interestingly we find that the Hofer-Zehnder capacity does not see the covering, i.e. the capacity of the disk tangent bundle of the lens space coincides with the capacity of the disk tangent bundle of the 3-sphere covering it. In particular, this gives a first example, where Gromov width and Hofer-Zehnder capacity of a disk tangent bundle disagree. Techniques we use include for the lower bound magnetic billiards and for the upper bound Gromov-Witten invariants.

Cited by

• On the contact type conjecture for exact magnetic systems

Related

• Hofer-Zehnder capacity of magnetic disc tangent bundles over constant curvature surfaces
• Hofer-Zehnder capacity of disc tangent bundles of projective spaces
• On the Hofer-Zehnder capacity for twisted tangent bundles over closed\n surfaces
• Gromov width of the disk cotangent bundle of spheres of revolution
• Hofer-Zehnder capacity of unit disk cotangent bundles and the loop product