Hamiltonian Floer Theory for Nonlinear Schrödinger Equations and the Small Divisor Problem

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