Liouville's Theorem through Symplectic Geometry

Liouville's theorem in classical mechanics is almost immediate in its symplectic geometry incarnation. Here I describe why!
In the previous video, I introduced Lie derivatives on vector fields, including a
derivation that the symplecitc form is preserved under Hamiltonian flow: • Lie derivatives of dif...
In the sequel, I talk about a cute consequence of Liouville's theorem, Poincare recurrence: • Poincare recurrence