Institute for Mathematical Sciences

Preprint ims91-8

J. Graczyk & G. Swiatek
Critical Circle Maps Near Bifurcation.

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 H\"{o}lder continuous function of the parameter. AMS subject code: 54H20
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