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Critical circle maps near bifurcation. (English) Zbl 0857.58034
The article gives estimates of the harmonic scalings in the parameter space of a one-parameter family of critical circle maps. The two main theorems which are proved state that the rotation number as a function of the parameter of the family of circle maps is Hölder continuous and that the Hausdorff dimension of the complement of the frequency-locking set is less than 1 but not less than $$1/3$$. The paper also studies the harmonic scalings in parameter space. Upper and lower universal bounded geometry estimates are proved.

##### MSC:
 37G99 Local and nonlocal bifurcation theory for dynamical systems
##### Keywords:
critical circle map; rotation number; Hausdorff dimension
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##### References:
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