Chaotic geodesic flow — square table with circular scatterer
The Sinai billiard is a square with a circular obstacle removed from the centre. A point particle bounces elastically off the walls and the circle. The circular scatterer creates exponential divergence of nearby trajectories (positive Lyapunov exponent), making this one of the first rigorously proven chaotic systems (Sinai 1970). Multiple nearby trajectories separate quickly, illustrating sensitivity to initial conditions.