Phase space: (or state space) Allows representation of the behaviour of a system in geometric form. The number of dimensions required for the phase space is a function of the "degrees of freedom" of the system.
A dynamical system consists in two parts: the notions of a state (the essential information about a system) and a dynamic (a rule that describes how the state evolves with time). This evolution can be visualized in a phase space. Phase spaces can have any number of dimensions, corresponding to the “degrees of freedom” of the system. The figures drawn in the phase space that describe the system's behavior are phase portraits.