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arXiv · 1305.3141

Floer homology for non-resonant magnetic fields on flat tori

Urs Frauenfelder·Will J. Merry·Gabriel P. Paternain
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Abstract

In this article we define and compute the Novikov Floer homology associated to a non-resonant magnetic field and a mechanical Hamiltonian on a flat torus T^{2N}. As a result, we deduce that this Hamiltonian system always has 2N+1 contractible solutions, and generically even 2^{2N} contractible solutions. Moreover if there exists a non-degenerate non-contractible solution then there necessarily exists another.

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Urs Frauenfelder, Will J. Merry, Gabriel P. Paternain. 2013-05-14. Floer homology for non-resonant magnetic fields on flat tori. https://arxiv.org/abs/1305.3141

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