Degenerate lower dimensional invariant tori in reversible system

Shengqing Hu; Bin Liu

doi:10.3934/dcds.2018162

Article Contents

2018, Volume 38, Issue 8: 3735-3763. Doi: 10.3934/dcds.2018162

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Degenerate lower dimensional invariant tori in reversible system

Shengqing Hu^, and
Bin Liu

School of Mathematical Sciences, Peking University, Beijing 100871, China

* Corresponding author: Shengqing Hu
* Corresponding author: Shengqing Hu

Received: June 2017

Revised: January 2018

Published: May 2018

The second author is supported by NNSF grant 11231001

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Abstract

In this paper, we are concerned with the existence of lower dimensional invariant tori in nearly integrable reversible systems. By KAM method, we prove that under some reasonable assumptions, there are many so-called degenerate lower dimensional invariant tori, that is one of normal frequencies is zero.

Keywords:

Reversible systems,
degenerate lower dimensional invariant tori,
KAM iteration.

Mathematics Subject Classification: Primary: 37J40; Secondary: 70K43.

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References

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