Standard Map: 2nd Poincaré Integral Invariant
The second Poincaré integral invariant
\[I_{2} = \int_{S} d\theta \wedge dp\]
of the Chirikov standard map, for four values of the stochasticity parameter K, computed over a square surface centred on (π, π). As for the first invariant, the map conserves I₂ exactly and the figures show the resolution of its numerical quadrature on the advected surface.
K = 0.6
K = 0.971635
K = 1.2
K = 2.0
