Variational destruction of invariant circles

Lin Wang

doi:10.3934/dcds.2012.32.4429

Article Contents

2012, Volume 32, Issue 12: 4429-4443. Doi: 10.3934/dcds.2012.32.4429

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Variational destruction of invariant circles

Lin Wang^1,

1.
Department of Mathematics, Nanjing University, No. 22 Hankou Road, Nanjing, 210093

Received: May 31, 2011

Revised: October 31, 2011

Published: November 2012

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Abstract

We construct a sequence of generating functions $(h_n)_{n\in\mathbb{N}}$, arbitrarily close to an integrable system in the $C^r$ topology with $r<4$ for $n$ large enough. With the variational method, we prove that for a given rotation number $\omega$ and $n$ large enough, the exact monotone area-preserving twist maps generated by $(h_n)_{n\in\mathbb{N}}$ admit no invariant circles with rotation number $\omega$.

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Mathematics Subject Classification: Primary: 58F27, 58F05; Secondary: 58F30.

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References

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