Non intersecting phase space trajectories

[geet89]

The phase space trajectories of an autonomous system of equations don't intersect.

Can this be proved mathematically.

Also what is the physical significance of this statement. What happens if they intersect?

 

[olivermsun]

The phase space trajectories of an autonomous system of equations don't intersect.

Can this be proved mathematically.

Also what is the physical significance of this statement. What happens if they intersect?

Hint: What would happen if you had two trajectories departing from the same point (which is another way of saying that there are intersecting trajectories)?