Phase Space/Sympletic Manifold

From Vectorcalcumb

Pair (M,W) where M is a differentiable manifold, and W is a closed, no degenerate differential 2-form on M. (pg. 62)

Phase spaces are never compact. Tourus/Sphere example? (pg. 62)

2 examples:

1) particle on line:2D plane w/ area form (pg.20)

2) n particles on line: R^(2n) w/ symplectic form (pg. 39)