Chaos Lab

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.

Chirikov standard map at K = K_c ≈ 0.9716. Each colour is one trajectory.

Equations

p_{n+1} = p_n + K sin θ_n
θ_{n+1} = θ_n + p_{n+1}    (mod 2π)

At a glance

ParametersK ≥ 0
Chaotic forK > K_c ≈ 0.9716 (global chaos)
HistoryChirikov (1979); fundamental to the KAM and Lazutkin theorems.

Try it

Open the interactive playground at /tools/standard-map.

See also

Quick quiz

Test yourself on standard

8 multiple-choice questions. Pick an answer for each, then submit to see explanations.

  1. Q1.The Chirikov standard map at K below K_c shows mostly:

  2. Q2.K_c was estimated numerically as:

  3. Q3.The standard map is:

  4. Q4.Physically the standard map describes:

  5. Q5.Above K_c the system has:

  6. Q6.KAM theory says:

  7. Q7.Greene's residue criterion estimates K_c by:

  8. Q8.Anomalous transport above K_c is characterised by:

0 of 8 answered