Quantitative destruction of invariant circles

Lin Wang

doi:10.3934/dcds.2021164

Article Contents

2022, Volume 42, Issue 3: 1569-1583. Doi: 10.3934/dcds.2021164

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Quantitative destruction of invariant circles

Lin Wang

School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China

Received: February 28, 2021

Revised: July 31, 2021

Early access: November 2021

Published: March 2022

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

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References

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