# Critical points of a Hamiltonian system

1. Aug 18, 2010

### 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..

2. Aug 19, 2010

### Eynstone

I think Liouville's theorem will put this through.