Z Skrypty dla studentów Ekonofizyki UPGOW

The Hénon map is a discrete-time dynamical system. It is one of the most studied examples of dynamical systems that exhibit chaotic behavior. The Hénon map takes a point (x_n, y_n) in the plane and maps it to a new point

\[\begin{align} x_{n+1} &= y_n+1-a x_n^2,\\ y_{n+1} &= b x_n. \end{align}\]

The map depends on two parameters, a and b, which for the canonical Hénon map have values of a = 1.4 and b = 0.3. For the canonical values the Hénon map is chaotic. For other values of a and b the map may be chaotic, intermittent, or converge to a periodic orbit. An overview of the type of behavior of the map at different parameter values may be obtained from its orbit diagram.