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2 Simple Maps     continued...

In Figure 8 we show a plot of the standard map for k = 1, obtained purely from relatively low-order periodic orbits [8].

Figure 8 The standard map for , obtained entirely from periodic orbits (whose periods are ). Notice the regular regions at the top and bottom (for , p = 0 and 1.0), at , and q=0 and 1.0, and at various other smaller regions. The ``jumble'' of points in other regions is indicative of chaotic behavior.

Figure 8: The standard map for k= 1.0 obtained entirely from periodic orbits.

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