Floer homology for non-resonant magnetic fields on flat tori

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 $\mathbb{T}^{2N}$. 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.