Variational destruction of invariant circles
L Wang - arXiv preprint arXiv:1106.6137, 2011 - arxiv.org
arXiv preprint arXiv:1106.6137, 2011•arxiv.org
We construct a sequence of generating functions $(h_n) _ {n\in\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\N} $
admit no invariant circles with rotation number $\omega $.
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\N} $
admit no invariant circles with rotation number $\omega $.
We construct a sequence of generating functions $(h_n)_{n\in\N}$, arbitrarily close to an integrable system in the topology with for large enough. With the variational method, we prove that for a given rotation number and large enough, the exact monotone area-preserving twist maps generated by $(h_n)_{n\in\N}$ admit no invariant circles with rotation number .
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