Standard map

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Example of the mapping of ten orbits of the Standard map for k = 2.0. The large green region is the main chaotic region of the map.
Example of the mapping of ten orbits of the Standard map for k = 2.0. The large green region is the main chaotic region of the map.

The standard (or Taylor-Chirikov) map is an area preserving chaotic map from a square with the side 2π into itself. It is defined by:

\begin{align} x_{n+1} &= x_n + k \sin(y_n), \\ y_{n+1} &= x_{n+1} + y_n \; (\mod 2\pi) \end{align}

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