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.
Famous quotes containing the word motion:
“till disproportion’d sin
Jarr’d against natures chime, and with harsh din
Broke the fair musick that all creatures made
To their great Lord, whose love their motion sway’d
In perfect Diapason, whilst they stood
In first obedience, and their state of good.”
—John Milton (1608–1674)