Critical circle maps near bifurcation
  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. 
Jacek Graczyk, Grzegorz Swiatek