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引用次数: 2
摘要
对于环空上的保面积扭转映射，我们考虑了用阶数为\begin{document}$ N $\end{document}的扰动\begin{document}$ R_N $\end{document}与\begin{document}$ \|R_N\|_{C^r}的三角多项式对给定频率\begin{document}$ \omega $\end{document}的不变圆的定量破坏问题。得到了\begin{document}$ N $\end{document}、\begin{document}$ r $\end{document}、\begin{document}$ epsilon $\end{document}与\begin{document}$ \omega $\end{document}的算术性质之间的关系，使得保面积映射不允许有\begin{document}$ \omega $\end{document}的不变圆。
For area-preserving twist maps on the annulus, we consider the problem on quantitative destruction of invariant circles with a given frequency \begin{document}$ \omega $\end{document} of an integrable system by a trigonometric polynomial of degree \begin{document}$ N $\end{document} perturbation \begin{document}$ R_N $\end{document} with \begin{document}$ \|R_N\|_{C^r}<\epsilon $\end{document}. We obtain a relation among \begin{document}$ N $\end{document}, \begin{document}$ r $\end{document}, \begin{document}$ \epsilon $\end{document} and the arithmetic property of \begin{document}$ \omega $\end{document}, for which the area-preserving map admit no invariant circles with \begin{document}$ \omega $\end{document}.
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