The hamiltonian

The equation of motion:

This equation guarantees that trajectories don't intersect.

A separable Hamiltonian

A dynamics is invertible, left, if any point in phasespace is the image of a single point in phasespace. The dynamics is non-invertible, right, if the motion transforms two different points into a single point in phasespace.

Time-reversal symmetry causes microscopic reversibility, w_rs = w_sr.

Symplectic transformation