Poincaré section of the kicked rotor: p' = p + K sin θ, θ' = θ + p' (mod 2π). At small K, KAM tori survive. Near K ≈ 0.97 the last torus breaks. Above K ≈ 1, resonances overlap and a chaotic sea floods phase space.
Each color = one trajectory. 500 iterations per trajectory. Drag slider to see chaos onset.