Liouville's theorem states that the phase space of a Hamiltonian system does not contract, which implies that systems with attractors or dissipative behaviors cannot be accurately represented by Hamiltonians. Non-Hamiltonian behaviors, such as friction, are attributed to the neglect of certain degrees of freedom in the system. For example, in a damped pendulum, while the pendulum's motion eventually ceases, including the air molecules as degrees of freedom maintains the phase space volume. This highlights the importance of considering all relevant degrees of freedom to fully understand mechanical systems. The discussion emphasizes that all mechanical systems can be viewed as Hamiltonian when all degrees of freedom are accounted for.