The winding number of a map is defined by
which represents the average increase in the angle per unit time (average frequency). A system with a
Rational winding number is Mode-Locked, whereas a system
with an Irrational winding number is Quasiperiodic. Note
that since the Rationals are a set of zero Measure on any finite interval, almost all
winding numbers will be irrational, so almost all maps will be Quasiperiodic.
© 1996-9 Eric W. Weisstein