Arnold Tongues

Vladimir Arnold first investigated Arnold tongues in a model for kicked rotors. They are domains of stability with periodic motion around rational values for a circle map. These domains are mode-locked to an irrational driving frequency and have a constant rational winding number. A plot is shown of the coupling strength between and , versus the driving phase from to .

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DETAILS

The circle map is given by
,
where is computed mod 1 and is a constant.
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