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The scaling of Arnol'd tongues for differentiable homeomorphisms of the circle

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Abstract

We show both for diffeomorphisms of the circle and for differentiable homeomorphisms that are not diffeomorphisms, that the widths of the Arnol'd tongues in a one parameter family scale asq −3 whenq is the denominator of the rotation number.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Queen's University, K7L 3N6, Kingston, Ontario, Canada

    Leo B. Jonker

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  1. Leo B. Jonker
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Communicated by J.-P. Eckmann

Research supported by NSERC

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Jonker, L.B. The scaling of Arnol'd tongues for differentiable homeomorphisms of the circle. Commun.Math. Phys. 129, 1–25 (1990). https://doi.org/10.1007/BF02096776

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  • DOI: https://doi.org/10.1007/BF02096776

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