Critical points of a Hamiltonian system

[xeno_gear]

Hello. I'm studying for an ODE/PDE qualifier and I'm wondering how to do this problem. I feel like it should be pretty easy, but anyway..

Show that a Hamiltonian system in $$\mathbb{R}^{2n}$$ has no asymptotically stable critical points.

Any suggestions? Thanks..

 

[Eynstone]

I think Liouville's theorem will put this through.