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Quantitative destruction of invariant circles

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  • 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 $.

    Mathematics Subject Classification: Primary: 37J50, 37E40.


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