Resonant tori of arbitrary codimension for quasi-periodically forced systems

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• 作者：Livia Corsi ; Guido Gentile
• 关键词：Mathematics Subject Classification34C45 ; 34C23 ; 37J40 ; 70H08 ; 70H33
• 刊名：Nonlinear Differential Equations and Applications NoDEA
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：24
• 期：1
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis;
• 出版者：Springer International Publishing
• ISSN：1420-9004
• 卷排序：24

文摘

We consider a system of rotators subject to a small quasi-periodic forcing. We require the forcing to be analytic and satisfy a time-reversibility property and we assume its frequency vector to be Bryuno. Then we prove that, without imposing any non-degeneracy condition on the forcing, there exists at least one quasi-periodic solution with the same frequency vector as the forcing. The result can be interpreted as a theorem of persistence of lower-dimensional tori of arbitrary codimension in degenerate cases.