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Hi everyone: I have a question about a proof in Siburg's paper "Symplectic Capacities in Two Dimensions". We define a admissible Hamiltonian $H$ in such a way that near from the boundary of a compact surface $M$, $H$ is constant, say $m(h)$. It's easy to see that if $x$ is solution curve of the associated Hamilton equation, such that $x(0)\in H^{-1}(h),$ where $h$ is a regular valur of $H$, then for all $t\in R,$ $x(t)\in H^{-1}(h)$. But, here is a statment that I do not understand why it's true:

By definition $H =m(H)$ near $\partial M$, so for each $h$ regular value of $H$. the set $H^{-1}(h)$ is a disjoint union of finitely many embedded circles...

I appreciate any suggestion. Best,

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thank you very much! – jdcastillo Dec 31 '12 at 21:20

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