Critical circle maps near bifurcation |
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| Authors: | Jacek Graczyk Grzegorz Swiatek |
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| Affiliation: | (1) Math Department, Warsaw University, ul. Banacha 2, Warszawa 59, Poland;(2) Mathematics Department, Princeton University, 08544 Princeton, NJ, USA;(3) Present address: Department of Mathematics, Pennsylvania State University, 16802 University Park, PA, USA |
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| 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.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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