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

Oliver Fabert*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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.

Original languageEnglish
Article numberrnab053
Pages (from-to)12220-12252
Number of pages33
JournalInternational Mathematics Research Notices
Volume2022
Issue number16
Early online date19 Apr 2021
DOIs
Publication statusPublished - Aug 2022

Bibliographical note

Publisher Copyright:
© 2021 The Author(s) 2018.

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