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.

中文翻译：

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非线性薛定谔方程和小除数问题的哈密顿弗洛尔理论

我们使用哈密顿弗洛尔理论的伪全纯曲线方法证明了非线性薛定谔方程的无限多时间周期解的存在。为了将 Gromov-Floer 紧致性定理推广到无限维，我们展示了如何通过将椭圆方法与丢番图近似理论的结果相结合来解决出现的小除数问题。