Interesting idea, and I'll look into it, but I think that that was just a coincidence. Taking another one of the problematic sections, we see that it occurs lower down:
I'm generating poincare sections of a double pendulum, and they mostly look okay, but some of them have weird discontinuities that seem wrong.
The condition for these sections is the standard ##\theta_1 = 0## and ##\dot{\theta}_1 > 0##. Looking at one of the maps, we see that most of the...