@ecterrab Hello Edgardo,

I have tried over 50 different sets of ics, they all reproduce the same effect. The only ones that don't produce this effect are those for extremely large energy (H = energy) which is not what i want. (I am trying to explore low energy values).

I have also explored the 'scene' option. However considering i am taking a p2-q2 section of a p2-q2-q1 3d plane it does not allow me to put any restrictions on p1. What you are suggesting only cuts the 'cube' of the phase space plot in half, it does not remove the negative p1 values and still shows there intersection of the section.

@ecterrab Hello Edgardo,

The method you specified does work, however the time intervals where p1>0 are so small that only one point is being mapped for each time chunk. In order to get an accurate map, i would need to do thousands of these.

Above, the map for p1>0 over t=-50..50.
Below, poincare map over interval -2..2. Similar results for all other time intervals.

@ecterrab Hello Edgardo,

Thank you for your reply. I'm afraid i was unsuccesful in finding an exact solution for the system, either one does not exist or my computer doesn't have the proccessing power to calculate it. I did however experiment with different time intervals, it would seem the value of p1 alternates between positive and negative values which is problematic. If you know a way to modify the time interval the take different "chunks" of time, ie. t=[0..4],[8..12] etc that might be helpful.

Thanks again.

@acer Thanks for the reply. I used:

ics:= generate_ic(H, {t=0.0, p2=-1.5..1.5, q1=0.0, q2=-0.5..0.5, energy = -7.3},20);

But this was chosen arbitrarily, any other set of initial conditions would suffice.