Phase space
A phase space is an abstract space containing all possible states of a dynamical system1, e.g. a Differential system. The evolution of a system forwards (and backwards) in time is determined completely for any point in the phase space. This path within the phase space is called a Trajectory. Since every point in the phase space is a possible state, every point must lie on exactly one trajectory, which yields strong geometric restrictions on the form of the trajectories, for example, trajectories cannot intersect in finite time.
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