Arnold Tongue
Consider the Circle Map. If 
is Nonzero, then the motion is periodic in some Finite regionsurrounding each rational 
. This execution of periodic motion in response to an irrational forcing is known asMode Locking. If a plot is made of versus with the regions of periodic Mode-Locked parameter space plotted around rational values (the Winding Numbers),then the regions are seen to widen upward from 0 at 
to some Finite width at 
. The region surroundingeach Rational Number is known as an Arnold Tongue.
At , the Arnold tongues are an isolated set of Measure zero. At , they form a general Cantor Set of dimension 
. In general, an Arnold tongue is defined as a resonance zone emanating outfrom Rational Numbers in a two-dimensional parameter space of variables.
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