← Labs
Ergodic Billiard Trajectories
Integrable vs chaotic billiards — Poincaré sections reveal KAM tori vs chaotic sea
Billiard Domain
Circle
Ellipse
Stadium
Sinai
Particles:
3
Pause
Trail length:
150
Circle billiard: integrable. Angular momentum conserved. Trajectory forms a chord pattern — never fills phase space chaotically.
Poincaré Section (x, v_x at y=0)
Clear Section
Add Particle
Bounce count:
0 bounces
Integrable: KAM tori → points trace smooth curves (invariant tori). Chaotic: points scatter ergodically (BGS conjecture). Click to add trajectory at clicked position.