Dynamical system

A dynamical system is a set of variables (a vector in phase space) whose values change with time according to some predetermined rules (the equations of motion). #m/def/dynamics Two main forms are the Differential system (continuous real time)

˙ 𝐱 = 𝑓 (𝐱)

and the Iterated map (discrete time)

𝐱 𝑛 + 1 = 𝑓 (𝐱 𝑛)

The fundamental difference is that in the differential case $𝑓$ describes the rate of change (hence it is sometimes called a velocity field) whereas for an iterated map it describes the change itself.

Properties

Fixed point

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