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On invariant sets in Lagrangian graphs |
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| Authors: | XiaoJun Cui Lei Zhao |
| Institution: | 1. Department of Mathematics, Nanjing University, Nanjing, 210093, China 2. Mathematisches Institut, Albert-Ludwigs-Universit?t, Freiburg im Breisgau, 79104, Germany 3. ASD, IMCCE, Paris Observatory, Paris, 75014, France 4. Department of Mathematics, Paris 7 University, Paris, 75013, France |
| Abstract: | In this exposition, we show that the Hamiltonian is always constant on a compact invariant connected subset which lies in a Lagrangian graph provided that the Hamiltonian and the graph are sufficiently smooth. We also provide some counterexamples to show that if the Hamiltonian function is not smooth enough, then it may be non-constant on a compact invariant connected subset which lies in a Lagrangian graph. |
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