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arXiv · 0911.5720

On invariant sets in Lagrangian graphs

Xiaojun Cui·Lei Zhao
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Abstract

In this exposition, we show that a Hamiltonian is always constant on a compact invariant connected subset which lies in a Lagrangian graph provided that the Hamiltonian and the graph are smooth enough. We also provide some counterexamples for the case that the Hamiltonians are not smooth enough.

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Xiaojun Cui, Lei Zhao. 2009-11-30. On invariant sets in Lagrangian graphs. https://doi.org/10.1007/s11425-010-4085-5

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