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

Abstract

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.

more details on the normal bundle argument, more direct proof of prop 7.1 illustrating the interplay between small divisors and regularizing nonlinearities, link with Floer's proof of the degenerate Arnold conjecture