Standard Map — Chirikov-Taylor

Canonical area-preserving map · KAM theory · chaos onset
Chaos parameter k k = 0.60
Iterations per orbit 500
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The standard map p' = p + k·sin(θ), θ' = θ + p' is the paradigm of Hamiltonian chaos. For small k, KAM tori (smooth curves) survive. As k increases, resonance islands (chains of closed regions) appear and tori progressively break. Above k ≈ 0.97 (Chirikov threshold), the last KAM torus breaks, connecting chaotic sea fills phase space.