The winding number of a map with initial value 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.