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        <center><img src=../../gif_files/GRAD_BLUE_LINE_f.gif></center>
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\begin{center}
        {\LARGE\bf Map in 2-Dimensions }
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        <center><img src=../../gif_files/GRAD_BLUE_LINE_f.gif></center>
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The Poincare Surface of Section projection of the trajectories characterized
by given energies in the Henon Heiles potential form a {\em 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
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<a href=../henon_map.c>henon_map.c</a>
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implements this map.
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Reference: {\em An introduction to Dynamical systems} by Arrowsmith and Place
has a section on this map.

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