The
dynamical system concept is a
mathematical formalization for any fixed "rule" which describes the
time dependence of a point's position in its ambient
space. The concept unifies very different types of such "rules" in mathematics: the different choices made for how time is measured and the special properties of the
ambient space may give an idea of the vastness of the class of objects described by this concept. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the ambient space may be simply a
set, without the need of a
smooth space-time structure defined on it.