Discrete map · 2D · dim 2
Standard (Chirikov) map
Chirikov's twist map of a kicked rotator. The canonical example of Hamiltonian chaos and the transition from integrable to mixed to chaotic phase space.
Equations
p_{n+1} = p_n + K sin θ_n
θ_{n+1} = θ_n + p_{n+1} (mod 2π)At a glance
| Parameters | K ≥ 0 |
|---|---|
| Chaotic for | K > K_c ≈ 0.9716 (global chaos) |
| History | Chirikov (1979); fundamental to the KAM and Lazutkin theorems. |
Try it
Open the interactive playground at /tools/standard-map.