The phase space is the set of all possible states of the system... along with the rules for moving from one state to the next.
It may be that not all states will be available to every initial condition.
It is possible that the trajectories are manifestations of a conservation principle that acts locally to a region in the phase space.
But this is a pretty general topic ... part of the field of topology iirc. Did you have any particular kind of phase space in mind?