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An infinite dimensional KAM theorem with application to two dimensional completely resonant beam equation

Dynamical Systems 2018-08-15 v1

Abstract

In this paper we consider the completely resonant beam equation on \T^2 with cubic nonlinearity on a subspace of L^2 (\T^2) which will be explained later. We establish an abstract infinite dimensional KAM theorem and apply it to the completely resonant beam equation. We prove the existence of a class of Whitney smooth small amplitude quasi-periodic solutions corresponding to finite dimensional tori.

Keywords

Cite

@article{arxiv.1701.05725,
  title  = {An infinite dimensional KAM theorem with application to two dimensional completely resonant beam equation},
  author = {Jiansheng Geng and Shidi Zhou},
  journal= {arXiv preprint arXiv:1701.05725},
  year   = {2018}
}

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26 pages