Hamiltonian Floer theory for nonlinear Schrödinger equations and the small divisor problem

We prove the existence of infinitely many time-periodic solutions of nonlinear Schrödinger equations using pseudo-holomorphic curve methods from Hamiltonian Floer theory. For the generalization of the Gromov-Floer compactness theorem to infinite dimensions, we show how to solve the arising small divisor problem by combining elliptic methods with results from the theory of diophantine approximations.

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