| 16 | On invariant sets in Lagrangian graphs显示文摘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. | CUI XiaoJun 1,2, & ZHAO Lei 3,4 1 Department of Mathematics, Nanjing University, Nanjing 210093, China 2 Mathematisches Institut, Albert-Ludwigs-Universita¨t, Freiburg im Breisgau 79104, Germany 3 ASD, IMCCE, Paris Observatory, Paris 75014, France 4 Department of Mathematics, Paris 7 University, Paris 75013, France | 2010 | Science China Mathematics2010，53，12： | 0 |
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