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arXiv · 2011.09828

On the Hofer-Zehnder capacity for twisted tangent bundles over closed surfaces

Johanna Bimmermann
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Abstract

We determine the Hofer-Zehnder capacity for twisted tangent bundles over closed surfaces for (i) arbitrary constant magnetic fields on the two-sphere and (ii) strong constant magnetic fields for higher genus surfaces. On $S^2$ we further give an explicit $\text{SO}(3)$-equivariant compactification of the twisted tangent bundle to $S^2\times S^2$ with split symplectic form. The former is the phase space of a charged particle moving on the two-sphere in a constant magnetic field, the latter is the configuration space of two massless coupled angular momenta.

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Johanna Bimmermann. 2020-11-19. On the Hofer-Zehnder capacity for twisted tangent bundles over closed surfaces. https://arxiv.org/abs/2011.09828

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