Stroboscopic Plot

[kushal]

Hello,

For a 2d phase-space, we say that the orbits are regular if the
stroboscopic plot of the orbits are closed curves and not area
filling. How do we generalize this idea to 4d phase space? Suppose we
have a set of equations:

x''= -x - x^2 y -x^3 +2*q*x*cos(2t)
y''= -y - x y^2 -y^3 +2*q*y*cos(2t)

where, q<<1 is a constant. Can we say that the stroboscopic plot of
the orbit in (x,v_x,y,v_y) phase space will lie on some 3d surface in
the 4d space? If yes, then can we also say that the stroboscopic plot
will be dense on this 3d sub-space?

Thanks,
Kushal.