Chirikov Standard Map — Poincaré Section: KAM Tori, Islands & Chaotic Sea

K = 0.50 Orbits: — Chaos: K > 0.97 → global Lyapunov: —

Nonlinearity K: 0.50
Iterations per orbit: 500
Orbit count: 50
Color: By orbit By Lyapunov By time step Redraw Reset K=0 Click canvas to add orbit

Chirikov standard map: p_{n+1} = p_n + K·sin(q_n), q_{n+1} = q_n + p_{n+1} (mod 2π). At K=0: integrable (circles). Increasing K breaks tori via KAM theorem — rational tori (resonances) become island chains. At K≈0.97 the last KAM torus (golden ratio) breaks → global chaos (Arnold diffusion).