Hamiltonian Chaos — Standard Map & KAM Tori

Chirikov standard map: p' = p + K·sin(θ), θ' = θ + p' (mod 2π)

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The Chirikov standard map is the canonical model of Hamiltonian chaos. For K<K_c=0.9716 (KAM regime) invariant tori persist, confining orbits to smooth curves. Above K_c the last KAM torus (golden mean winding number) breaks, and chaotic regions percolate across phase space. Click canvas to trace a single orbit.