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.

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1999-05-26