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| Lagrange Stability and KAM Tori for Duffing Equations with Quasi-periodic Coefficients |
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Citation： |
Huining XUE,Xiaoping YUAN.Lagrange Stability and KAM Tori for Duffing Equations with Quasi-periodic Coefficients[J].Chinese Annals of Mathematics B,2025,46(3):359~372 |
| Page view： 248
Net amount： 106 |
Authors： |
Huining XUE; Xiaoping YUAN |
Foundation： |
the National Natural Science Foundation of China (Nos. 12071254,12371189) |
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| Abstract： |
It is proved that there are many (positive Lebesgue measure)
Kolmogorov-Arnold-Moser (KAM for short) tori at infinity
and thus all solutions are bounded for the Duffing equations
$\ddot{x}+x^{2n+1}+\sum\limits_{j=0}^{2n}p_i(t) {x^{j}} =0$ with
$p_j(t)$'s being time-quasi-periodic smooth functions. |
Keywords： |
KAM tori Lagrangian stability Duffing equation Quasi-periodic function |
Classification： |
37J40, 34C11 |
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