Why can't phase space trajectories intersect?

[Apashanka]

Phase space trajectories can't intersect each other is it due to the fact that at the intersection point there will be more than one possible path for the system to evolve with time??

 

[hilbert2]

Yes, it's because of that. In an autonomous system, that is, where you can set the origin of the time coordinate wherever you want without changing anything, the time evolution has to be uniquely determined by the initial position in phase space.