The equations of motion of the kicked rotator write d θ θ d t = ∂ ∂ H ∂ ∂ p = p I and d p d t = − − ∂ ∂ H ∂ ∂ θ θ = K sin ⁡ ⁡ θ θ ∑ ∑ n = − − ∞ ∞ ∞ ∞ δ δ ( t T − − n ) Theses equations show that between two consecutive kicks, the rotator simply moves freely: the momentum p is conserved and the angular position growths linearly in time. On the other hand, during each kick the momentum abruptly jumps by a quantity K T sin ⁡ ⁡ θ θ , where θ θ is the angular position near the kick. The kicked rotator dynamics can thus be described by the discrete map p n + 1 = p n + K T sin ⁡ ⁡ θ θ n and θ θ n + 1 = θ θ n + T I p n + 1 where θ θ n and p n are the canonical coordinates at time t = n T − − , just before the n -th kick. It is usually more convenient to introduce dimensionless momentum p → → p / I T , time t → → t / T and kicking strength K → → K / I T 2 to reduce the dynamics to the single parameter map p n + 1 = p n + K sin ⁡ ⁡ θ θ n and θ θ n + 1 = θ θ n + p n + 1 known as Chirikov standard map, with the caveat that p n is not periodic as in the standard map. However, one can directly see that two rotators with same initial angular position θ θ 0 but shifted dimensionless momentum p 0 and p 0 + 2 π π l (with l an arbitrary integer) will have the same exact stroboscopic dynamics, but with dimensionless momentum shifted at any time by 2 π π l (this is why stroboscopic phase portraits of the kicked rotator are usually displayed in a single momentum cell p ∈ ∈ [ − − π π , π π ] ).