Floer homology for non-resonant magnetic fields on flat tori
Frauenfelder, Urs · Merry, Will J. · Paternain, Gabriel P.
Original · EN
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 T²ⁿ. As a result, we deduce that this Hamiltonian system always has 2N+1 contractible solutions, and generically even 2²ⁿ contractible solutions. Moreover if there exists a non-degenerate non-contractible solution then there necessarily exists another.
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