Standard map

The standard map (also known as the Chirikov–Taylor map or as the Chirikov standard map) is an area-preserving chaotic map from a square with side ${\displaystyle 2\pi }$ onto itself. It is constructed by a Poincaré's surface of section of the kicked rotator, and is defined by:

${\displaystyle p_{n+1}=p_{n}+K\sin(\theta _{n})}$

${\displaystyle \theta _{n+1}=\theta _{n}+p_{n+1}}$

where ${\displaystyle p_{n}}$ and ${\displaystyle \theta _{n}}$ are taken modulo ${\displaystyle 2\pi }$.

The properties of chaos of the standard map were established by Boris Chirikov in 1969.