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.
