  We prove the existence of infinitely many time-periodic solutions of
nonlinear Schr\"odinger 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.
