Collisions: 0
Lyapunov (approx): —
Sinai billiard: a particle bounces in a square with a circular obstacle removed from the center. The convex obstacle defocuses trajectories — nearby rays diverge exponentially.
Ergodicity: almost every trajectory visits every region with equal time average = space average (proved by Sinai 1970, Bunimovich-Sinai 1980).
Comparison: switch to "Rectangular" mode to see an integrable billiard where trajectories are quasi-periodic and do NOT fill the table ergodically.
ACF: autocorrelation of vx(t) — decays exponentially for Sinai, shows oscillations for rectangular.
Ergodicity: almost every trajectory visits every region with equal time average = space average (proved by Sinai 1970, Bunimovich-Sinai 1980).
Comparison: switch to "Rectangular" mode to see an integrable billiard where trajectories are quasi-periodic and do NOT fill the table ergodically.
ACF: autocorrelation of vx(t) — decays exponentially for Sinai, shows oscillations for rectangular.