Is this a correct expansion of what you are saying: Liouville's theorem says the phase space of a Hamiltonian system doesn't contract, so systems with attractors or dissipative systems can't be represented by Hamiltonians - but in principle the non-Hamiltonain behaviour comes from ignoring degrees of freedom?Liouville's theorem applies to all mechanical systems if you don't ignore degrees of freedom.
Yes, as far as we know, all mechanical systems are Hamiltonian. Non-Hamiltonian behavior (like friction, for example) is assumed to be due to ignoring degrees of freedom.Is this a correct expansion of what you are saying: Liouville's theorem says the phase space of a Hamiltonian system doesn't contract, so systems with attractors or dissipative systems can't be represented by Hamiltonians - but in principle the non-Hamiltonain behaviour comes from ignoring degrees of freedom?