Map in 2-Dimensions

The Poincare Surface of Section projection of the trajectories characterized by given energies in the Henon Heiles potential form a Map in 2-dimensions.

Frocschle (1968) and Henon (1969) were among the first to try to abstract the features of Henon Heiles potential SOS in $y$ and $p_y$ via an artificial map in 2-dimensions. Let $x$ and $y$ be the variables. The map transforms the ($x$,$y$) plane into itself. Thus a point ($x$,$y$) is mapped into ($x$,$y$) via

$$x_1 = x cos(\alpha) - ( y-x^2 ) sin(\alpha)$$

$$y_1 = x sin(\alpha) + ( y-x^2 ) cos(\alpha)$$

$\alpha$ is a parameter..

The skeleton code henon_map.c \begin{rawhtml} implements this map.

Reference: An introduction to Dynamical systems by Arrowsmith and Place has a section on this map.

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