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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 differential forms   In the sequel, I talk about a cute consequence of Liouville's theorem, Poincare recurrence:    • Poincare recurrence