Billiards#

Examples illustrating the five 2D billiard geometries in physicskit.chaos.systems.billiards: a trajectory bouncing inside each shape, and the boundary phase-space (Poincare) section that distinguishes integrable geometries (Circle, Rectangle) from chaotic, defocusing ones (Sinai, Bunimovich Stadium, Truncated Circle).

Bunimovich Stadium (Chaotic)

Bunimovich Stadium (Chaotic)

Circle Billiard (Integrable)

Circle Billiard (Integrable)

Ellipse Billiard (Integrable, with Caustics)

Ellipse Billiard (Integrable, with Caustics)

Extreme Sensitivity: a Slightly Truncated Circle

Extreme Sensitivity: a Slightly Truncated Circle

Comparing All Five Billiards

Comparing All Five Billiards

Rectangle Billiard (Integrable)

Rectangle Billiard (Integrable)

Sinai Billiard (Chaotic)

Sinai Billiard (Chaotic)

Truncated Circle Billiard (Mixed Phase Space)

Truncated Circle Billiard (Mixed Phase Space)