On the Hofer-Zehnder capacity for twisted tangent bundles over closed surfaces · arXivDesk
2011.09828Nov 19, 2020The results of this paper are now contained in arXiv:2311.00467 for the part about twisted tangent bundles over surfaces and in paper arXiv:2306.11382 for the part on the symplectomorphism between the twisted tangent bundle of $S^2$ and $S^2\times S^2$ with split symplectic form. The proof presented in arXiv:2311.00467 is very different and much shorter than the proof in this draft
On the Hofer-Zehnder capacity for twisted tangent bundles over closed surfaces
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 S2 we further give an explicit SO(3)-equivariant compactification of the twisted tangent bundle to S2×S2
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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.