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arXiv · 2109.08785

Quantitative destruction of invariant circles

Lin Wang
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Abstract

For area-preserving twist maps on the annulus, we consider the problem on quantitative destruction of invariant circles with a given frequency $\omega$ of an integrable system by a trigonometric polynomial of degree $N$ perturbation $R_N$ with $\|R_N\|_{C^r}<\epsilon$. We obtain a relation among $N$, $r$, $\epsilon$ and the arithmetic property of $\omega$, for which the area-preserving map admit no invariant circles with $\omega$.

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Lin Wang. 2021-09-17. Quantitative destruction of invariant circles. https://arxiv.org/abs/2109.08785

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