Ergodic mixing — particle visits all regions uniformly
Billiard table (particle trajectory)
Poincaré section (s, sin θ)
The Bunimovich stadium is a rectangle of width 2a capped with two unit semicircles. Proved ergodic and mixing by Bunimovich (1979). The Poincaré section plots (s, sin θ) where s is arclength position and θ is angle with the boundary normal — uniform filling = ergodicity.