Example 2: The Henon Map

In this example, we use the Mathcad to plot a sample (chaotic) trajectory of the Henon map superimposed on a set of critical curves. This is done very simply without any programming, and gives a sense of why the Henon attractor looks the way that it does. Same ideas and similar commands naturally apply to other maps. For more intensive calculations involving lots of critical curves, the worksheet discussed here will not be sufficient, and even some programming may be necessary (possible in Mathcad Professional or Premium versions). For more on critical curves, see the 1996 book by C. Mira et al, or the 1997 book by R. Abraham et al, both listed in the Books Corner.

We start with a definition of the Henon map H(x,y), and a description of the commands that generate the first few critical curves and a sample trajectory:

The plot of the sample trajectory superimposed on the plot of the critical curves that the above commands generate is given below, followed by a portion of the time series:

Note:
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