Singularity results for functional equations driven by linear fractional   transformations
  We consider functional equations driven by linear fractional transformations, which are special cases of de Rham's functional equations. We consider Hausdorff dimension of the measure whose distribution function is the solution. We give a necessary and sufficient condition for singularity. We also show that they have a relationship with stationary measures. 
Kazuki Okamura
math.PR math.CA