Use this tag for questions related to almost periodic functions, which are functions of a real number that are periodic to within any desired level of accuracy given suitably long, well-distributed "almost-periods".
An almost periodic function is, loosely speaking, a function of a real number that is periodic to within any desired level of accuracy given suitably long, well-distributed, "almost periods." There is also a notion of almost periodic functions on locally compact abelian groups.
Almost periodicity is a property of dynamical systems that appear to retrace their paths through phase space, but not exactly. An example would be a system of planets with orbital periods that are not commensurable, i.e., with a period vector that is not proportional to a vector of integers. A theorem of Kronecker from Diophantine approximation can be used to show that any particular configuration that occurs once will recur to within any specified accuracy: if we wait long enough we can observe the planets return to within a second of an arc to the positions in which they once were.
