Scalings in circle maps III
  Circle maps with a flat spot are studied which are differentiable, even on the boundary of the flat spot. Estimates on the Lebesgue measure and the Hausdorff dimension of the non-wandering set are obtained. Also, a sharp transition is found from degenerate geometry similar to what was found earlier for non-differentiable maps with a flat spot to bounded geometry as in critical maps without a flat spot. 
Jacek Graczyk, Grzegorz Swiatek, Folkert Tangerman, J. J. P. Veerman