However, there is a flaw in this view of the oscillator. The forcing term has been ignored. At any point the forcing term could be adding energy to a trajectory that normally would not make it over the hump, and push it over, or the opposite, remove energy from a trajectory that would normally pass over the hump. Since the system is chaotic, we can't predict it's behavior with any accuracy. Our plot is probably out the window and will show nothing but a mess of points.
Lets try it anyways.
Instead it took a plot that would probably not be too interesting and twisted it up. Examining the plot for a while we see that it has symmetry about the origin. That is not unexpected. A maximum that is far to the right should produce the exact opposite behavior as a maximum that is far to the left. The physics behind this is that the system does not have enough energy to make it over the hump.