Abstract
We consider families of maps of the circle of degree 1 which are homeomorphisms but not diffeomorphisms, that is maps like
withc=1. We prove that the set of parameter values corresponding to irrational rotation numbers has Lebesgue measure 0. In other words, the intervals on which frequency-locking occurs fill up the set of full measure.
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Communicated by J.-P. Eckmann
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Świątek, G. Rational rotation numbers for maps of the circle. Commun.Math. Phys. 119, 109–128 (1988). https://doi.org/10.1007/BF01218263
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DOI: https://doi.org/10.1007/BF01218263