Quasiperiodic motion

In mathematics and theoretical physics, quasiperiodic motion is in rough terms the type of motion executed by a dynamical system containing a finite number (two or more) of incommensurable frequencies.

That is, if we imagine that the phase space is modelled by a torus "T", the trajectory of the system is modelled by a curve on "T" that wraps around without ever exactly coming back on itself.

A quasiperiodic function on the real line is the type of function (continuous, say) obtained from a function on "T", by means of a curve

:"R" → "T"

which is linear (when lifted from "T" to its covering Euclidean space), by composition. It is therefore oscillating, with a finite number of underlying frequencies. (NB the sense in which theta functions and the Weierstrass zeta function in complex analysis are said to have quasi-periods with respect to a period lattice is something distinct from this.)

The theory of almost periodic functions is, roughly speaking, for the same situation but allowing "T" to be a torus with an infinite number of dimensions.