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## Main Question or Discussion Point

As I understand it, the phase space is the space of all possible states, without reference to the rule of transformation from one state to another; whereas the phase portrait is the phase space with the paths from one state to another connected following the system's rule of transformation.

If that is so, then, for a classical system, is there only one path in the phase portrait between two states

If that is so, then, for a classical system, is there only one path in the phase portrait between two states

*A*and*B*over a fixed time interval from*t*to_{i}*t*?_{j}