scholarly journals A KAM theorem for the elliptic lower dimensional tori with one normal frequency in reversible systems

2017 ◽  
Vol 37 (4) ◽  
pp. 2141-2160
Author(s):  
Xiaocai Wang ◽  
◽  
Junxiang Xu ◽  
Dongfeng Zhang ◽  
Keyword(s):  
Reversible Systems ◽  
Kam Theorem ◽  
Normal Frequency ◽  
Lower Dimensional Tori ◽  
Lower Dimensional

scholarly journals A KAM theorem without action-angle variables for elliptic lower dimensional tori

Nonlinearity ◽  
2011 ◽  
Vol 24 (4) ◽  
pp. 1033-1080 ◽  
Author(s):  
Alejandro Luque ◽  
Jordi Villanueva
Keyword(s):  
Kam Theorem ◽  
Lower Dimensional Tori ◽  
Lower Dimensional

On the persistence of degenerate lower-dimensional tori in reversible systems

2014 ◽  
Vol 35 (7) ◽  
pp. 2311-2333 ◽  
Author(s):  
XIAOCAI WANG ◽  
JUNXIANG XU ◽  
DONGFENG ZHANG
Keyword(s):  
Differential Equation ◽  
Invariant Torus ◽  
Special Structure ◽  
Reversible Systems ◽  
Small Perturbations ◽  
Normal Matrices ◽  
Lower Dimensional Tori ◽  
Lower Dimensional

This work focuses on the persistence of lower-dimensional tori with prescribed frequencies and singular normal matrices in reversible systems. By the Kolmogorov–Arnold–Moser theory and the special structure of unperturbed nonlinear terms in the differential equation, we prove that the invariant torus with given frequency persists under small perturbations. Our result is a generalization of X. Wang et al [Degenerate lower dimensional tori in reversible systems. J. Math. Anal. Appl.387 (2012), 776–790].

scholarly journals Degenerate lower dimensional tori in reversible systems

2012 ◽  
Vol 387 (2) ◽  
pp. 776-790 ◽  
Author(s):  
Xiaocai Wang ◽  
Junxiang Xu ◽  
Dongfeng Zhang
Keyword(s):  
Reversible Systems ◽  
Lower Dimensional Tori ◽  
Lower Dimensional
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