Abstract
We estimate harmonic scalings in the parameter space of a one-parameter family of critical circle maps. These estimates lead to the conclusion that the Hausdorff dimension of the complement of the frequency-locking set is less than 1 but not less than 1/3. Moreover, the rotation number is a Hölder continuous function of the parameter.
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Communicated by M. Herman
Partially supported by KBN grant “Iteracje i Fraktale” #210909101.
Partially supported by NSF Grant #DMS-9206793 and the Sloan Research Fellowship.
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Graczyk, J., Swiatek, G. Critical circle maps near bifurcation. Commun.Math. Phys. 176, 227–260 (1996). https://doi.org/10.1007/BF02099548
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DOI: https://doi.org/10.1007/BF02099548