HAMILTONIAN BILLIARDS
Trajectories in bounded tables — chaos vs. integrability
Billiards: a point particle bouncing elastically off walls. Square/circle = integrable (regular orbits, conserved quantities).
Ellipse = integrable (trajectories stay tangent to a confocal ellipse/hyperbola — caustics).
Stadium (Bunimovich 1974) = fully chaotic (ergodic, mixing, positive Lyapunov exponent).
Click to launch from that point.