A KAM theorem for the Hamiltonian with finite zero normal frequencies and its applications
Dynamical Systems
2019-08-30 v1
Abstract
In this paper, we investigate the existence of KAM tori for an infinite dimensional Hamiltonian system with finite number of zero normal frequencies. By constructing a constant quantity we show that, for "most" frequencies in the sense of Lebesgue measure, either if the quantity is zero, there is a KAM tori or if the quantity is not zero, there is no KAM tori in some domain. As application, we show that the nonlinear Schr\"{o}dinger equation with a zero frequency possesses many quasi-periodic solutions.
Keywords
Cite
@article{arxiv.1908.11072,
title = {A KAM theorem for the Hamiltonian with finite zero normal frequencies and its applications},
author = {Yuan Wu and Xiaoping Yuan},
journal= {arXiv preprint arXiv:1908.11072},
year = {2019}
}