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Liouville's Theorem

The idea of this animation is to give an example of Liouville's theorem in phase space. The Hamiltonian is sin(p) + sin(x). We start out with a circle with radius 5 centered at the origin. In particular, it should be the case that none of the interior points (colored red) ever "cross" the boundary (colored black). Of course, I can only animate a finite number of points (in this case 1000 boundary points). But hopefully, it gives the basic picture. For more information, go to: https://PhysicsCafe.org